https://pipmath.app/ 2026-10-24 https://pipmath.app/privacy/ 2026-10-22 https://pipmath.app/learn-algebra-visually/ 2026-10-24 https://pipmath.app/graphing-functions-game/ 2026-10-24 https://pipmath.app/solve-equations-visually/ 2026-10-24 https://pipmath.app/guides/ 2026-10-22 https://pipmath.app/solve-inequalities-visually/ 2026-10-24 https://pipmath.app/graph-transformations-visually/ 2026-10-24 https://pipmath.app/quadratics-visually/ 2026-10-24 https://pipmath.app/polynomials-visually/ 2026-10-22 https://pipmath.app/exponentials-and-logs-visually/ 2026-10-22 https://pipmath.app/sine-and-cosine-visually/ 2026-10-22 https://pipmath.app/limits-visually/ 2026-10-22 https://pipmath.app/derivatives-visually/ 2026-10-22 https://pipmath.app/integrals-visually/ 2026-10-22 https://pipmath.app/blog/ 2026-10-24 https://pipmath.app/blog/find-slope-from-two-points/ 2026-10-23 https://pipmath.app/blog/find-slope-from-two-points/slope-poster.jpg How to find the slope from two points, explained in under a minute Rise over run: divide the change in height by the change across between any two points to get the slope. https://pipmath.app/blog/find-slope-from-two-points/slope-vertical.mp4 52 2026-10-23 yes https://pipmath.app/blog/what-is-a-function/ 2026-10-23 https://pipmath.app/blog/what-is-a-function/function-poster.jpg What is a function in math, explained in under a minute A function is a rule that gives exactly one output for every input. The vertical line test shows which graphs are functions. https://pipmath.app/blog/what-is-a-function/function-vertical.mp4 57 2026-10-23 yes https://pipmath.app/blog/what-does-f-of-x-mean/ 2026-10-23 https://pipmath.app/blog/what-does-f-of-x-mean/fx-poster.jpg What does f(x) mean, explained in under a minute f(x) is the output of the function f for the input x. f(4) means put 4 in, not f times 4. https://pipmath.app/blog/what-does-f-of-x-mean/fx-vertical.mp4 48 2026-10-23 yes https://pipmath.app/blog/domain-and-range-explained/ 2026-10-23 https://pipmath.app/blog/domain-and-range-explained/domain-poster.jpg Domain and range explained simply, in under a minute The domain is the shadow of a graph on the floor, the inputs allowed. The range is its shadow on the wall, the outputs that come out. https://pipmath.app/blog/domain-and-range-explained/domain-vertical.mp4 51 2026-10-23 yes https://pipmath.app/blog/what-is-slope/ 2026-10-23 https://pipmath.app/blog/what-is-slope/slope-meaning-poster.jpg What is slope in math, explained in under a minute Slope is how far a line goes up or down for every step across: rise over run. Uphill is positive, downhill is negative, flat is zero. https://pipmath.app/blog/what-is-slope/slope-meaning-vertical.mp4 50 2026-10-23 yes https://pipmath.app/blog/slope-intercept-form/ 2026-10-23 https://pipmath.app/blog/slope-intercept-form/mxb-poster.jpg Slope-intercept form y = mx + b, explained in under a minute In y = mx + b, m is the slope and b is where the line crosses the y-axis. Change m and the line pivots, change b and it slides. https://pipmath.app/blog/slope-intercept-form/mxb-vertical.mp4 43 2026-10-23 yes https://pipmath.app/blog/graph-a-line-from-its-equation/ 2026-10-23 https://pipmath.app/blog/graph-a-line-from-its-equation/graph-line-poster.jpg How to graph a line from its equation, in under a minute Start at b on the y-axis, step across 1 and up by the slope, repeat, then draw the line through the dots. https://pipmath.app/blog/graph-a-line-from-its-equation/graph-line-vertical.mp4 51 2026-10-23 yes https://pipmath.app/blog/equation-of-a-line-from-two-points/ 2026-10-24 https://pipmath.app/blog/equation-of-a-line-from-two-points/equation-poster.jpg How to find the equation of a line from two points, in under a minute Find the slope from the two points, put one point into y = mx + b to find b, then check the equation with the other point. https://pipmath.app/blog/equation-of-a-line-from-two-points/equation-vertical.mp4 53 2026-10-23 yes https://pipmath.app/blog/horizontal-and-vertical-lines-slope/ 2026-10-23 https://pipmath.app/blog/horizontal-and-vertical-lines-slope/special-lines-poster.jpg Slope of horizontal and vertical lines, in under a minute A horizontal line has a rise of 0, so its slope is 0. A vertical line has a run of 0, so its slope is undefined. https://pipmath.app/blog/horizontal-and-vertical-lines-slope/special-lines-vertical.mp4 52 2026-10-23 yes https://pipmath.app/blog/how-to-solve-a-linear-equation/ 2026-10-23 https://pipmath.app/blog/how-to-solve-a-linear-equation/solve-poster.jpg How to solve a linear equation, in under a minute Each side of an equation is a line. Doing the same to both sides moves both lines, but they still cross at the same x, the answer. https://pipmath.app/blog/how-to-solve-a-linear-equation/solve-vertical.mp4 55 2026-10-23 yes https://pipmath.app/blog/x-intercept-and-y-intercept/ 2026-10-24 https://pipmath.app/blog/x-intercept-and-y-intercept/intercepts-poster.jpg How to find the x-intercept and y-intercept, in under a minute The y-intercept is where a line crosses the y-axis, so set x to 0. The x-intercept is where it crosses the x-axis, so set y to 0 and solve. https://pipmath.app/blog/x-intercept-and-y-intercept/intercepts-vertical.mp4 45 2026-10-23 yes https://pipmath.app/blog/is-it-a-linear-function/ 2026-10-23 https://pipmath.app/blog/is-it-a-linear-function/linear-test-poster.jpg How to tell if a function is linear, in under a minute A function is linear when the output changes by the same amount for every step of the input. Check the differences in a table. https://pipmath.app/blog/is-it-a-linear-function/linear-test-vertical.mp4 47 2026-10-23 yes https://pipmath.app/blog/linear-word-problems/ 2026-10-23 https://pipmath.app/blog/linear-word-problems/word-problems-poster.jpg How to solve linear equation word problems, in under a minute The price per visit is the slope and the joining fee is b, so a gym that costs 20 to join and 5 per visit is y = 5x + 20. Six visits cost 50, and 70 buys 10 visits. https://pipmath.app/blog/linear-word-problems/word-problems-vertical.mp4 47 2026-10-23 yes https://pipmath.app/blog/parallel-and-perpendicular-lines/ 2026-10-23 https://pipmath.app/blog/parallel-and-perpendicular-lines/parallel-perpendicular-poster.jpg Parallel and perpendicular lines, in under a minute Parallel lines have the same slope. When two lines meet at a right angle, their slopes multiply to −1: flip the fraction and change the sign. https://pipmath.app/blog/parallel-and-perpendicular-lines/parallel-perpendicular-vertical.mp4 45 2026-10-23 yes https://pipmath.app/blog/solve-a-system-of-equations-by-graphing/ 2026-10-23 https://pipmath.app/blog/solve-a-system-of-equations-by-graphing/system-graphing-poster.jpg How to solve a system of equations by graphing, in under a minute Each equation is a line. The solution is the point where the lines cross. y = 2x − 2 and y = −x + 7 cross at (3, 4), which works in both equations. https://pipmath.app/blog/solve-a-system-of-equations-by-graphing/system-graphing-vertical.mp4 39 2026-10-23 yes https://pipmath.app/blog/solve-a-system-by-substitution/ 2026-10-24 https://pipmath.app/blog/solve-a-system-by-substitution/substitution-poster.jpg How to solve a system by substitution, in under a minute For y = 3x and x + y = 8, replace y with 3x to get x + 3x = 8. That gives x = 2, and then y = 6, so the solution is (2, 6). https://pipmath.app/blog/solve-a-system-by-substitution/substitution-vertical.mp4 37 2026-10-23 yes https://pipmath.app/blog/no-solution-or-infinitely-many-solutions/ 2026-10-23 https://pipmath.app/blog/no-solution-or-infinitely-many-solutions/no-solution-poster.jpg No solution or infinitely many solutions, in under a minute Parallel lines have the same slope and never meet, so 2x + 1 = 2x − 3 gives 1 = −3, which is false: no solution. The same line gives 0 = 0, which is always true: infinitely many. https://pipmath.app/blog/no-solution-or-infinitely-many-solutions/no-solution-vertical.mp4 42 2026-10-23 yes https://pipmath.app/blog/break-even-point/ 2026-10-23 https://pipmath.app/blog/break-even-point/break-even-poster.jpg How to find the break-even point of two plans, in under a minute Plan A costs 10 plus 1 per GB and plan B costs 4 plus 3 per GB. They break even at 3 GB, where both cost 13. Plan B is cheaper before that and plan A after. https://pipmath.app/blog/break-even-point/break-even-vertical.mp4 39 2026-10-23 yes https://pipmath.app/blog/how-to-solve-a-linear-inequality/ 2026-10-23 https://pipmath.app/blog/how-to-solve-a-linear-inequality/inequality-poster.jpg How to solve a linear inequality, in under a minute 2x + 1 > 5 gives x > 2. When you divide both sides by a negative number, flip the inequality sign: −3x < 12 gives x > −4. https://pipmath.app/blog/how-to-solve-a-linear-inequality/inequality-vertical.mp4 44 2026-10-23 yes https://pipmath.app/blog/graph-an-inequality/ 2026-10-24 https://pipmath.app/blog/graph-an-inequality/graph-inequality-poster.jpg How to graph an inequality, in under a minute Graph y > x + 1 by drawing the boundary dashed, then testing a point. (1, 4) works, so shade that side. (3, 0) does not. https://pipmath.app/blog/graph-an-inequality/graph-inequality-vertical.mp4 47 2026-10-23 yes https://pipmath.app/blog/function-transformations-explained/ 2026-10-24 https://pipmath.app/blog/function-transformations-explained/transformations-poster.jpg Function transformations explained in under a minute Start with y = x². Inside the brackets, x − 1 slides it right 1. In front, −2 stretches it by 2 and flips it. At the end, + 3 lifts it up 3. https://pipmath.app/blog/function-transformations-explained/transformations-vertical.mp4 46 2026-10-24 yes https://pipmath.app/blog/vertical-shift-of-a-function/ 2026-10-24 https://pipmath.app/blog/vertical-shift-of-a-function/vertical-shift-poster.jpg Vertical shifts of a function in under a minute Adding 2 at the end of y = x² lifts every point up by 2. Subtracting 3 lowers every point by 3. The shape does not change, only the heights. https://pipmath.app/blog/vertical-shift-of-a-function/vertical-shift-vertical.mp4 34 2026-10-24 yes https://pipmath.app/blog/horizontal-shift-of-a-function/ 2026-10-24 https://pipmath.app/blog/horizontal-shift-of-a-function/horizontal-shift-poster.jpg Horizontal shifts of a function in under a minute In y = (x − 3)² the bottom of the bowl is where the inside is zero, at x = 3, so it slides 3 to the right. In y = (x + 2)² it is at x = −2, so it slides left. https://pipmath.app/blog/horizontal-shift-of-a-function/horizontal-shift-vertical.mp4 39 2026-10-24 yes https://pipmath.app/blog/reflect-a-graph-over-the-x-axis-and-y-axis/ 2026-10-24 https://pipmath.app/blog/reflect-a-graph-over-the-x-axis-and-y-axis/reflections-poster.jpg Reflecting a graph over the x-axis and y-axis in under a minute A minus in front flips y = √x over the x-axis, so (4, 2) goes to (4, −2). A minus on the x flips it over the y-axis, so (4, 2) goes to (−4, 2). https://pipmath.app/blog/reflect-a-graph-over-the-x-axis-and-y-axis/reflections-vertical.mp4 34 2026-10-24 yes https://pipmath.app/blog/vertical-stretch-and-compression/ 2026-10-24 https://pipmath.app/blog/vertical-stretch-and-compression/stretch-poster.jpg Stretching and squashing a graph in under a minute A 2 in front of x² multiplies every height by 2, so the parabola is taller and looks narrower. A ½ makes it flatter. A 2 on x squeezes it toward the y-axis. https://pipmath.app/blog/vertical-stretch-and-compression/stretch-vertical.mp4 38 2026-10-24 yes https://pipmath.app/blog/what-is-a-quadratic-function/ 2026-10-24 https://pipmath.app/blog/what-is-a-quadratic-function/quadratic-poster.jpg What is a quadratic function, in under a minute y = x² − 4x + 3 is a bowl because the number in front of x² is positive. It crosses the y-axis at 3 and its lowest point, the vertex, is at (2, −1). Make that number negative and it is an arch. https://pipmath.app/blog/what-is-a-quadratic-function/quadratic-vertical.mp4 40 2026-10-24 yes https://pipmath.app/blog/vertex-form-of-a-quadratic/ 2026-10-24 https://pipmath.app/blog/vertex-form-of-a-quadratic/vertex-form-poster.jpg Vertex form of a quadratic in under a minute In y = −2(x + 1)² + 8, the vertex is (h, k). Since x + 1 means h = −1, the vertex is (−1, 8) and the axis of symmetry is x = −1. https://pipmath.app/blog/vertex-form-of-a-quadratic/vertex-form-vertical.mp4 40 2026-10-24 yes https://pipmath.app/blog/roots-of-a-quadratic-factored-form/ 2026-10-24 https://pipmath.app/blog/roots-of-a-quadratic-factored-form/roots-poster.jpg Roots from the factored form of a quadratic in under a minute In y = (x − 1)(x − 5) a product is zero only when a bracket is zero, so the roots are 1 and 5, and the vertex is halfway, at x = 3. A plus bracket like x + 2 gives the root −2. https://pipmath.app/blog/roots-of-a-quadratic-factored-form/roots-vertical.mp4 44 2026-10-24 yes https://pipmath.app/blog/solve-a-quadratic-by-factoring/ 2026-10-24 https://pipmath.app/blog/solve-a-quadratic-by-factoring/factoring-poster.jpg How to solve a quadratic by factoring, in under a minute For x² − 5x + 6 = 0, find two numbers that multiply to 6 and add to −5: −2 and −3. It factors to (x − 2)(x − 3) = 0, so x = 2 or x = 3. https://pipmath.app/blog/solve-a-quadratic-by-factoring/factoring-vertical.mp4 37 2026-10-24 yes https://pipmath.app/blog/quadratic-formula-and-discriminant/ 2026-10-24 https://pipmath.app/blog/quadratic-formula-and-discriminant/formula-poster.jpg The quadratic formula and the discriminant in under a minute For x² − 2x − 3 = 0 the part under the root, b² − 4ac, is 16, so x = (2 ± 4) ÷ 2 = 3 or −1. When that number is positive there are two solutions, zero gives one, negative gives none. https://pipmath.app/blog/quadratic-formula-and-discriminant/formula-vertical.mp4 49 2026-10-24 yes https://pipmath.app/blog/point-slope-form/ 2026-10-24 https://pipmath.app/blog/point-slope-form/pointslope-poster.jpg Point-slope form y − y₁ = m(x − x₁), explained in under a minute Put the point and the slope into y − y₁ = m(x − x₁) to write the line at once, check it with another point, then open the bracket to get y = mx + b. https://pipmath.app/blog/point-slope-form/pointslope-vertical.mp4 52 2026-10-24 yes https://pipmath.app/blog/standard-form-of-a-line/ 2026-10-24 https://pipmath.app/blog/standard-form-of-a-line/standard-poster.jpg Standard form Ax + By = C: find the intercepts and graph the line, in under a minute Write a line as Ax + By = C, set y to 0 to find where it crosses the x-axis, set x to 0 for the y-axis, and join the two points. https://pipmath.app/blog/standard-form-of-a-line/standard-vertical.mp4 44 2026-10-24 yes https://pipmath.app/blog/solve-a-system-by-elimination/ 2026-10-24 https://pipmath.app/blog/solve-a-system-by-elimination/elimination-poster.jpg Solve a system of equations by elimination, in under a minute Add the two equations so that y cancels, solve for x, put x back to find y, and check the answer in both equations. https://pipmath.app/blog/solve-a-system-by-elimination/elimination-vertical.mp4 48 2026-10-24 yes https://pipmath.app/blog/absolute-value-equations/ 2026-10-24 https://pipmath.app/blog/absolute-value-equations/absolute-poster.jpg Absolute value equations and the V-shaped graph, in under a minute Absolute value is distance from zero. Graph y = |x| as a V, cut it with a horizontal line to solve |x| = 5, then slide the V to solve |x − 3| = 4. https://pipmath.app/blog/absolute-value-equations/absolute-vertical.mp4 46 2026-10-24 yes https://pipmath.app/blog/inverse-functions/ 2026-10-24 https://pipmath.app/blog/inverse-functions/inverse-poster.jpg Inverse functions: swap x and y, in under a minute An inverse function undoes the original. See the graph mirror over y = x, swap x and y to find the formula, and check it with a number. https://pipmath.app/blog/inverse-functions/inverse-vertical.mp4 46 2026-10-24 yes https://pipmath.app/blog/completing-the-square/ 2026-10-24 https://pipmath.app/blog/completing-the-square/square-poster.jpg Completing the square, in under a minute Take half of b, square it, add and subtract it, and x² + 6x + 5 becomes (x + 3)² − 4. Read the vertex off the graph, then solve by taking a square root. https://pipmath.app/blog/completing-the-square/square-vertical.mp4 56 2026-10-24 yes https://pipmath.app/about/ 2026-10-24