5.3  Write Equations of Lines Given two Points

Mrs. Agriesti's Algebra

Goal: To learn to use two points to write the equation of a line.

Example 1:  Write the equation of the line containing the points (-1,1) and (0,3).

Use the slope formula to find the slope.  Be careful with your signs.

Replace m with slope.
Replace x and y with the coordinates of one of the points.  (Either point is fine)

Solve for b (y-intercept).


Now write the equation using the slope and y-intercept (b).

  y = mx + b
  y = 2x + b
  1 = 2(-1) + b
  1 = -2 + b
+2   +2     
  3 = b

  y = mx + b
  y = 2x + 3

Example 2:  Write the equation of the line containing the points (4,4) and (-2, -1).

Use the slope formula to find the slope.  Be careful with your signs.


Replace m with slope.
Replace x and y with the coordinates of one of the points.  (Either point is fine)

Solve for b (y-intercept).




Now write the equation using the slope and y-intercept (b).

       y = mx + b
       y = (5/6)x + b
       4 = (5/6)(4) + b
       4 = 20/6 + b
       4 = 10/3 + b
  4      = 3 1/3 + b
-3 1/3  -3 1/3     
    2/3 = b

  y = mx + b
  y = (5/6)x + 2/3

Example 3:  Write the equation of the line containing the points (3,-4) and (3,8).

Use the slope formula to find the slope. 

The slope is undefined (no slope).  The line is a vertical line.  (See sections 4.1 and 4.4)

The equation for a vertical line is x = a. 

Our two points have 3 for their x-coordinate, therefore the equation is x = 3.