Ontario MTH1W · Algebra · C4.4
Determine equations of lines
Use slope and a point to write and apply the equation of a line.
The core idea
In y = mx + b, m is the slope and b is the y-intercept. Two points determine the slope; substituting either point then reveals the intercept.
Learning example
Build an equation from two points
Find the equation of the line through (2, 1) and (6, 9).
- 1
Find the slope: m = (9 − 1) ÷ (6 − 2) = 8 ÷ 4 = 2.
- 2
Use y = 2x + b and substitute (2, 1): 1 = 2(2) + b.
- 3
Solve for b: 1 = 4 + b, so b = −3.
Answery = 2x − 3
A common mistake
Dividing the change in x by the change in y. Slope is change in y divided by change in x.
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