Mathematics — first biennium · Lesson
In y=ax+b, a controls slope and b is the y-intercept. A point lies on the line if its coordinates satisfy the formula.
Prerequisites: Functions, coordinates and equations
Goal: Read slope and intercept and construct points on a line.
In this lesson: Read slope and intercept and construct points on a line.
New concept: In the line y=ax+b, a is the slope: it measures the change in y when x increases by 1 (more generally a=Δy/Δx). If a>0 the line rises from left to right, if a<0 it falls, and if a=0 it is horizontal. b is the y-intercept: the value of y when x=0, hence where the line meets the y-axis. To find a point, substitute x into the formula, calculate y, and write the ordered pair (x,y).
How to proceed: Do not swap a and b: a multiplies x; b is the value of y when x=0.
You can already assume: Functions, coordinates and equations.
Move m to change the line's slope and direction; change q to move the y-intercept.
With a = 0 the curve loses this family's characteristic shape; also try a non-zero value.
The graph connects slope, intercept and points on the line to the formula y=ax+b.
Completed exercises: 0/5 · Correct on first attempt: 0
Do not swap a and b: a multiplies x; b is the value of y when x=0.
Data / situation: y=4x+0; use x=-3.
ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.
Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.