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

Explanation:

Answer 2

`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 equation of the solid line

we have the coordinates (0,2) and (4,-1)

Find the slope m

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute

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

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

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

Find the equation of the line in slope intercept form

`y=mx=b`

where

m is the slope

b is the y-intercept (value of y when the value of x is equal to zero)

we have

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

`b=2` ---> is given

substitute

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

Remember that

The shading area is below the 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