Algebra I

Writing Equations: Slope-Intercept Form

Lesson

The slope-intercept form of a linear equation is:

y = mx + b

where $m$ is the slope and $b$ is the y-intercept — the value of $y$ when $x = 0$ .

To write the equation of a line given two points:

Find the slope $m$ using the slope formula.
Plug $m$ and one of the points into $y = mx + b$ and solve for $b$ .
Write the final equation with both values plugged in.

Worked example 1

Write the equation through $(1, 5)$ and $(3, 11)$ .

Slope:

m = \frac{11 - 5}{3 - 1} = \frac{6}{2} = 3

Plug $m = 3$ and the point $(1, 5)$ into $y = mx + b$ :

5 = 3(1) + b

b = 2

Final equation:

y = 3x + 2

Worked example 2

Write the equation through $(0, -4)$ and $(2, 0)$ .

Slope:

m = \frac{0 - (-4)}{2 - 0} = \frac{4}{2} = 2

Notice the y-intercept is given directly — at $x = 0$ we have $y = -4$ , so $b = -4$ .

y = 2x - 4

How to type your answer

Write the equation in standard slope-intercept form: y, equals, slope times x, plus or minus b. No spaces. Examples: y=3x+2, y=2x-4, y=-x+5. For a horizontal line, just write y=7.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

(0, 0) \text{ and } (1, 5)

Problem 2

(0, 1) \text{ and } (1, 4)

Problem 3

(0, -2) \text{ and } (1, 1)

Problem 4

(0, 4) \text{ and } (2, 8)

Practice

Standard problems matching the lesson.

Problem 5

(1, 5) \text{ and } (3, 11)

Problem 6

(0, -4) \text{ and } (2, 0)

Problem 7

(0, 3) \text{ and } (4, 11)

Problem 8

(2, 7) \text{ and } (5, 16)

Problem 9

(1, 1) \text{ and } (4, -8)

Problem 10

(0, 0) \text{ and } (2, 6)

Problem 11

(-1, 4) \text{ and } (1, 0)

Problem 12

(2, 5) \text{ and } (4, 5)

Problem 13

(0, -2) \text{ and } (3, 7)

Problem 14

(-2, 1) \text{ and } (0, 5)

Problem 15

(1, -2) \text{ and } (3, 4)

Problem 16

(0, 1) \text{ and } (5, -4)

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 17

(-2, -1) \text{ and } (1, 8)

Problem 18

(3, 1) \text{ and } (-1, 9)

Problem 19

(2, -3) \text{ and } (5, 6)

Problem 20

(-3, 5) \text{ and } (3, -7)

Problem 21

(1, 0) \text{ and } (4, 9)

Problem 22

(-4, 3) \text{ and } (2, -3)

Practice

Standard problems matching the lesson.

Problem 23

A taxi fare is 5 dollars at 0 miles and 13 dollars at 4 miles. Write y = mx + b for fare y after x miles.

Problem 24

A plant is 3 cm tall at week 0 and 11 cm tall at week 4. Write y = mx + b for height y at week x.

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 25

A car's odometer reads 30 mi at hour 0 and 210 mi at hour 3. Write y = mx + b for the reading y at hour x.

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