Algebra is easier when you can see it. Every straight line y = ax + b is a path with a starting height and a steepness. Drag the sliders and watch Pip walk it.
Free to start. Coming soon to the App Store.
Every line y = ax + b begins somewhere on the y-axis. Put x = 0 into the rule and the ax part disappears, so only b is left. That is why b is the point where the line crosses the y-axis.
Try it in the graph above: drag Start b and watch the gold dot slide up and down the y-axis.
Setting x to 0 leaves only b, so b is exactly where the line crosses the y-axis.
The number a tells you how steep the line is. Take one step to the right and the line goes up by a. Two steps, two a. Every stair on the line is the same height, which is exactly why a line is straight.
A bigger a makes a steeper line. A negative a takes the line downhill. And a = 0 gives a flat line.
Each step of 1 to the right adds a, so a is the height of every stair on the line.
Pick any two points on a line. How far up you go is the rise. How far across you go is the run. Divide the rise by the run and you get the slope.
Pick two different points and you get the same number, because a straight line never changes steepness.
Dividing the change in height by the change across between any two points gives you the slope.
The y-intercept is the point where a line crosses the y-axis. In y = ax + b it is b, because putting x = 0 into the rule leaves only b.
The slope is how much the line goes up for every step to the right. In y = ax + b it is a. A positive slope goes uphill, a negative slope goes downhill, and a slope of 0 is a flat line.
Divide the rise (how far up) by the run (how far across). From (0, 1) to (3, 4) the rise is 3 and the run is 3, so the slope is 3 ÷ 3 = 1. Any two points on the same line give the same answer.
It is the rule for a straight line: pick any x, multiply it by a, add b, and you get y. The number a sets the steepness and b sets the starting height.
In Pip: Math Adventure, a line is a bridge. You choose its slope and its starting height so it rests on both banks, and Pip walks across. A wrong answer is acted out, so you see why it failed and not only that it did.
It 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.