Mathematics · Grades 7–10

Linear graphs: slope, intercept and checks

Connect an equation, its graph and a table without guessing from appearance.

Understand the idea

Requires different x values; preserve the same subtraction order.

m = (y₂ − y₁)/(x₂ − x₁)

From (1,3) to (4,9): m = 6/3 = 2.

For a nonvertical line, b is the y value when x = 0.

y = mx + b

y = 2x − 5 crosses the y-axis at (0,−5).

Use a known point and slope.

y − y₁ = m(x − x₁)

Through (2,7) with m = 3: y − 7 = 3(x − 2).

All points have the same y coordinate.

y = c has slope 0

y = 4 passes through (−2,4) and (5,4).

The slope quotient would divide by zero.

x = c has undefined slope

x = −3 passes through (−3,1) and (−3,8).

Check both coordinates in the original relation.

A point lies on the line when its coordinates satisfy the equation.

(3,1) lies on y = 2x − 5 because 1 = 6 − 5.