The Pip blog
A short course in teaching order: functions first, then lines, then equations. Every post has a live graph, worked examples, the mistakes to avoid and a short video. For the full picture, see the twelve guides.
Functions
What is a function in math?
A function is a rule with one answer for every input. The machine, the table, the graph and the vertical line test, with a live graph.
Part 2 · 5 min readWhat does f(x) mean?
f(x) is the output for the input x. How to evaluate a function from a rule, a table and a graph, and how to work backwards.
Part 3 · 6 min readDomain and range, explained simply
The domain is the inputs a function accepts, the range is the outputs it gives. Find both from a list, a graph and a rule.
Lines
What is slope in math?
Slope is how steep a line is and which way it leans. Rise over run, with positive, negative and zero slope and a live graph.
Part 5 · 5 min readHow to find the slope from two points
The slope formula, step by step, with a live graph, worked examples, the mistakes to avoid and three practice questions.
Part 6 · 6 min readSlope-intercept form: y = mx + b, explained
y = mx + b: m is the slope, b is where the line starts on the y-axis. Read it, write it and rearrange to it, with a live graph.
Part 7 · 6 min readHow to graph a line from its equation
Start at b on the y-axis, then step by the slope. Three worked examples, including a fraction slope and an equation that needs rearranging.
Part 8 · 6 min readHow to find the equation of a line from two points
Slope first, then b. Three worked examples, a check with the other point, and a live graph where you move the second point.
Part 9 · 5 min readSlope of horizontal and vertical lines
A flat line has slope 0, an upright line has undefined slope. Why they differ, how to tell y = 3 from x = 3, and a live graph.
Equations
Learn it by playing
Pip: Math Adventure is a math game for iPhone, coming soon to the App Store. Join the list and we will tell you the day Pip is out.