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Explanation
[tex]\begin{gathered} y\leq-2x-3 \\ y>4x+7 \end{gathered}[/tex]Step 1
First, graph the inequality 1
[tex]y\leq-2x-3[/tex]the related equation is
[tex]y=-2x-3[/tex]now, get 2 coordinates of the line
a) when x=1
[tex]\begin{gathered} y=-2x-3 \\ y=-2(1)-3 \\ y=-2-3 \\ y=-5 \\ so,\text{ the coordinate is (1,-5)} \end{gathered}[/tex]b)when x=0
[tex]\begin{gathered} y=-2x-3 \\ y=-2\cdot0-3 \\ y=0-3 \\ y=-3 \\ \text{coordinate P2}\Rightarrow(0,-3) \end{gathered}[/tex]now, draw a line that pases trought the coordinates we found.
Since the inequality is ≤ , not a strict one, the border line is solid
Step 2
Now, do the same for inequality 2
so
[tex]y>4x+7[/tex]the related equation is
[tex]y=4x+7[/tex]find 2 coordinates of the line
a)when x=0
[tex]\begin{gathered} y=4x+7 \\ y=4\cdot0+7 \\ y=0+7 \\ y=7 \\ so,\text{ the coordinate 3 is (0,7)} \end{gathered}[/tex]b) when x=-2
[tex]\begin{gathered} y=4x+7 \\ y=4\cdot-2+7 \\ y=-8+7 \\ y=-1 \\ so,\text{ the coordinate 4 is (-2},-1) \end{gathered}[/tex]now, draw the line 2, this lines passes trougth the coordiantes 3 and 4
Since the inequality is >, a strict one, the border line is dotted
Step 3
Graph:
in inequality (1) we need the values smaller r than -2x-3, it measn all values under the line,
and in Inequality 2 we need the values greater than 4x+7, it means all values over the line
so, the solution is the dark purple zone
I hope this helps you
