Question

Write an inequality to represent the graph.

a solid line passing through points 0 comma 2 and 4 comma negative 1 with shading below the line

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

Answer 1

`y \leq -(3)/(4)x+2`

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

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=-(3)/(4)`

step 2

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

`y=mx+b`

we have

`m=-(3)/(4)`

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

substitute

`y=-(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 -(3)/(4)x+2`

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