5.1 & 5.2  Write Equations of Lines Given the Slope and a Point

Mrs. Agriesti's Algebra

Goal: To learn to use the slope and any point on the line to write the equation of the line.

Example 1:

  y = mx + b
  y = 2x + b
-5 = 2(-1) + b
-5 = -2 + b
+2   +2     
-3 = b

y = mx + b
y = 2x - 3

I can see from the graph of the line that the slope is 2 (rise 2, run 1).

I can find many points on the line.  It doesn't matter which one I use.  I am going to use (-1, -5).

Plug the values in and solve for b.

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

Example 2: 

Write the equation of the line that passes through (8,3) with slope 4.

   y = mx + b
   y = 4x + b
   3 = 4(8) + b
   3 = 32 + b
-32   -32     
-29 = b

y = mx + b
y = 4x - 29

Replace m with slope.
Replace x and y with coordinates of point.
Solve for b (y-intercept).


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

Example 3: 

Write the equation of the line that passes through (6,7) with slope 2/3.

   y = mx + b
   y = (2/3)x + b
   7 = (2/3)(6) + b
   7 = 12/3 + b
   7 = 4 + b
  -4   -4     
   3 = b

y = mx + b
y = (2/3)x + 3

Replace m with slope.
Replace x and y with coordinates of point.

Solve for b (y-intercept).


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