Step 1. Graphing the first inequality.
The first inequality is:
[tex]y>3x+7[/tex]
to graph this, we need to graph the line 3x+7, which compared with the slope-intercept equation
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept, the line
[tex]y=3x+7[/tex]
is a line with a slope of 3 and a y-intercept at 7:
SInce the inequality is:
[tex]y>3x+7[/tex]
The solution just for this inequality are the values greater than the red line, but not including the red line so we represent is a dotted line and a shaded part above:
Step 2. Graph the second inequality.
The second inequality is:
[tex]y\le-3x-8[/tex]
As we did with the first inequality, we graph the line -3x-8 first.
comparing -3x-8 with the slope-intercept equation:
[tex]y=mx+b[/tex][tex]y=-3x-8[/tex]
we can see that the slope m is -3 and the y-intercept b is -8. This line is shown in blue in the following diagram along with our results for the previous inequality:
Since the inequality form is:
[tex]y\le-3x-8[/tex]
We shade the values below this blue line:
The final solution will be the intersection between the red part and the blue part:
