Question

Write an inequality to represent the graph.

Answer 1

Answer:

$y \leq -\frac{3}{4}x+2$

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

$m=(-1-2)/(4-0)$

$m=-\frac{3}{4}$

step 2

Find the linear equation of the solid line in slope intercept form

$y=mx+b$

we have

$m=-\frac{3}{4}$

$b=2$ ---> the y-intercept is given

substitute

$y=-\frac{3}{4}x+2$

step 3

Find the inequality

Remember that the solution is the shaded area below the solid line

therefore

The inequality is

$y \leq -\frac{3}{4}x+2$

y is less than or equal to negative three fourths times x plus 2