Answer:
Graph 1 -----> [tex]y \leq -3x-3[/tex]
Graph 2 ----> [tex]y<\frac{2}{3}x+1[/tex]
Graph 3 ----> [tex]y>2x-4[/tex]
Graph 4 -----> [tex]y \geq \frac{x}{3}+3[/tex]
Step-by-step explanation:
Graph 1) we know that
The solution is the shaded area below (to the left) the solid line
The slope of the solid line is negative
The y-intercept of the solid line is (0,-3)
The x-intercept of the solid line is (-1,0)
The equation of the solid line is [tex]y=-3x-3[/tex]
therefore
The inequality is
[tex]y \leq -3x-3[/tex]
Graph 2) we know that
The solution is the shaded area below the dashed line
The slope of the dashed line is positive
The y-intercept of the dashed line is (0,1)
The x-intercept of the dashed line is (-1.5,0)
The equation of the dashed line is [tex]y=\frac{2}{3}x+1[/tex]
therefore
The inequality is
[tex]y<\frac{2}{3}x+1[/tex]
Graph 3) we know that
The solution is the shaded area above the dashed line
The slope of the dashed line is positive
The y-intercept of the dashed line is (0,-4)
The x-intercept of the dashed line is (2,0)
The equation of the dashed line is [tex]y=2x-4[/tex]
therefore
The inequality is
[tex]y>2x-4[/tex]
Graph 4) we know that
The solution is the shaded area above the solid line
The slope of the solid line is positive
The y-intercept of the solid line is (0,3)
The x-intercept of the solid line is (-9,0)
The equation of the solid line is [tex]y=\frac{x}{3}+3[/tex]
therefore
The inequality is
[tex]y \geq \frac{x}{3}+3[/tex]
