4.5  Quick Graphs Using the Slope-Intercept Form

Mrs. Agriesti's Algebra

Goal:  To use the slope-intercept form to graph linear equations.

y-intercept - The point where the line crosses the y-axis.

To sketch the line:

1. Get the equation in slope-intercept form.  (Solve for y.)
   
2. On the y-axis plot the y-intercept (b).
   
3. Use the slope to plot a few more points.
   

Sketch each line:

8x - 4y = 12

8x - 4y = 12                First solve for y.
-8x          -8x
     - 4y = -8x + 12       -8x and 12 are not like terms.
     - 4y = -8x + 12       Divide all terms by -4
      - 4      -4      -4
        y = 2x - 3


Now that the equation is in slope-intercept form you know the slope is 2 and the y-intercept is -3. 

Plot the y-intercept on the y-axis.

Change the slope to a fraction and use it to plot a few more points. 

3x + 4y - 12 = 0

3x + 4y - 12 =  0                 Solve for y.
-3x         +12    -3x + 12
         4y        = -3x + 12     
         4y = -3x + 12              Divide all terms by 4
          4      4       4
           y = (-3/4)x + 3


Now that the equation is in slope-intercept form you know the slope is -3/4 and the y-intercept is 3. 

Plot the y-intercept on the y-axis.

Use the slope to plot a few more points.