All skills Math

Learn Index · Functions and Relations Grade 9–10

Slope-intercept form

y = mx + b where m is the slope and b is the y-intercept.

Read

The form

y = mx + b

  • m = slope (rise over run)
  • b = y-intercept (where the line crosses the y-axis)

This is slope-intercept form. With just m and b you can graph any non-vertical linear equation. The constants m and b are called parameters.

Reading m and b

Equation m b
y = 3x + 2 3 2
y = −x + 5 −1 5
y = ½x − 4 ½ −4
y = 7 0 7
y = −2x −2 0

Graphing from y = mx + b

Example: y = (2/3)x − 1

  1. Plot the y-intercept: (0, −1).
  2. Use rise over run: up 2, right 3 → (3, 1).
  3. Repeat: (6, 3).
  4. Draw a straight line through the points.

For a negative slope like −3/4, go down 3, right 4.

Writing the equation from a graph

  1. Read b where the line crosses the y-axis.
  2. Count rise and run between two clear points to find m.
  3. Write y = mx + b.

Writing the equation from two points

Example: through (2, 7) and (4, 11)

  1. m = (11 − 7)/(4 − 2) = 2
  2. Substitute one point: 7 = 2(2) + b → b = 3
  3. y = 2x + 3

Converting to slope-intercept form

Solve for y.

Example: 4x + 2y = 10

  • 2y = −4x + 10
  • y = −2x + 5

In context

A phone plan: C = 0.15t + 25 (t = texts).

  • b = $25: the monthly base fee (cost with zero texts)
  • m = $0.15: the cost per text

Effect of changing m and b

  • Changing b shifts the line up or down (parallel lines).
  • Changing m changes the steepness and direction.

Worked examples

Example 1: Slope and y-intercept of y = −4x + 9? m = −4, b = 9.

Example 2: Equation with slope 5 through (0, −2)? y = 5x − 2.

Example 3: Equation through (1, 4) with slope −3? 4 = −3 + b → b = 7 → y = −3x + 7.

Common mistakes

  • Reading b as the x-intercept.
  • Going the wrong way for negative slopes.
  • Forgetting to divide every term when solving for y.

Try it yourself

  1. Find m and b: y = ¾x − 6.
  2. Write the equation: m = −2, b = 8.
  3. Line through (0, 3) and (2, 11)?
  4. Rewrite 3x − y = 7 in slope-intercept form.
  5. A taxi: $4 plus $1.75/km. Write the equation.

Answers: 1) m = ¾, b = −6 2) y = −2x + 8 3) y = 4x + 3 4) y = 3x − 7 5) C = 1.75d + 4

Quick recap

  • Slope-intercept form: y = mx + b.
  • Plot b, then use rise over run from m.
  • In context, b is the starting value and m is the rate.