How to Write the Equation of a Line

Step-by-step solution

1. Write the point-slope form.

   $$y - y_1 = m(x - x_1)$$

   Why: This form uses the slope and one known point.

2. Substitute the slope and the point.

   $$y - 7 = 2(x - 3)$$

   Why: m is 2, x_1 is 3 and y_1 is 7.

3. Distribute the 2 on the right side.

   $$y - 7 = 2x - 6$$

   Why: 2 times x is 2x, and 2 times -3 is -6.

4. Add 7 to both sides.

   $$y = 2x + 1$$

   Why: Adding undoes the subtraction and gives slope-intercept form.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

1. 1

   $\text{Slope } 3 \text{ through } (1, 2)$

   Show answer

   $y = 3x - 1$

2. 2

   $\text{Slope } 2 \text{ through } (0, 5)$

   Show answer

   $y = 2x + 5$

3. 3

   $\text{Slope } -1 \text{ through } (2, 6)$

   Show answer

   $y = -x + 8$

4. 4

   $\text{Slope } 4 \text{ through } (2, 3)$

   Show answer

   $y = 4x - 5$

5. 5

   $\text{Slope } \frac{1}{2} \text{ through } (4, 5)$

   Show answer

   $y = \frac{1}{2}x + 3$