ALEKS PURPLE Graphing a linear inequality in the plane: Problem
type 1
For this type of problem, ALEKS will give you an inequality in standard form.
Graph  4x  7y  24
Make a point table and try various points (any points will do):
x
y
Let's try x = 1:
4(1)  7 y  24
4  7 y  24
4  4  7 y  24  4
7 y  28
7 y 28

7
7
y  4  That will be easy to plot (1, -4)
x
y
1
-4
Now let’s see if we can find another point without fractions:
Let's try y = 0:
4x  7(0)  24
4x  24
4x 24

4
4
x  6  That will be easy to plot (-6, 0)
x
y
1
-4
-6
0
Now you can plot this line. It will be dashed because the symbol of the original
inequality is > instead of > with the equal symbol.
To test the graph to see which side you shade, pick any point not on the line. I’ll use (0,
0)
4x  7 y  24
4  0   7  0   24
0  0  24
0  24 FALSE
Thus, the side of the line with (0, 0) is NOT shaded:
While you can graph an inequality in standard form by selecting multiple points as we
did above, it is sometimes easier to convert the equation to slope-intercept form to
graph it (when you can’t find two nice points to plot as we did above):
Graph
 4x  7 y  24
Add 4x to both sides to move the x to the right:
4x  4x  7 y  4x  24
4x 4x  7 y  4x  24
7 y  4x  24
Divide both sides by -7 to isolate the y:
(Remember to switch the inequality sign when dividing by a negative)
7 y
7

y 
4x 24

7 7
4
24
x 
7
7
The y-intercept is 
The slope is 
4
7
24
7
I’m not sure that helps in this case; however, sometimes the y-intercept and the slope
are not fractions and are easily graphed when in slope-intercept form.