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Algebra I

Writing Equations: Slope-Intercept Form

Lesson

The slope-intercept form of a linear equation is:

y=mx+by = mx + b

where mm is the slope and bb is the y-intercept — the value of yy when x=0x = 0.

To write the equation of a line given two points:

  1. Find the slope mm using the slope formula.
  2. Plug mm and one of the points into y=mx+by = mx + b and solve for bb.
  3. Write the final equation with both values plugged in.

Worked example 1

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

Slope:

m=11−53−1=62=3m = \frac{11 - 5}{3 - 1} = \frac{6}{2} = 3

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

5=3(1)+b5 = 3(1) + b
b=2b = 2

Final equation:

y=3x+2y = 3x + 2

Worked example 2

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

Slope:

m=0−(−4)2−0=42=2m = \frac{0 - (-4)}{2 - 0} = \frac{4}{2} = 2

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

y=2x−4y = 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) and (1,5)(0, 0) \text{ and } (1, 5)

Problem 2

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

Problem 3

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

Problem 4

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

Practice

Standard problems matching the lesson.

Problem 5

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

Problem 6

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

Problem 7

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

Problem 8

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

Problem 9

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

Problem 10

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

Problem 11

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

Problem 12

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

Problem 13

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

Problem 14

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

Problem 15

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

Problem 16

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

Challenge

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

Problem 17

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

Problem 18

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

Problem 19

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

Problem 20

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

Problem 21

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

Problem 22

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