Answer:
[tex]y \leq -\frac{3}{4}x+2[/tex]
y is less than or equal to negative three fourths times x plus 2
Step-by-step explanation:
step 1
Find the slope of the solid line
we have the ordered pairs
(0,2) and (4,-1)
Find the slope m
[tex]m=(-1-2)/(4-0)[/tex]
[tex]m=-\frac{3}{4}[/tex]
step 2
Find the linear equation of the solid line in slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=-\frac{3}{4}[/tex]
[tex]b=2[/tex] ---> the y-intercept is given
substitute
[tex]y=-\frac{3}{4}x+2[/tex]
step 3
Find the inequality
Remember that the solution is the shaded area below the solid line
therefore
The inequality is
[tex]y \leq -\frac{3}{4}x+2[/tex]
y is less than or equal to negative three fourths times x plus 2
