Question

Write an inequality to represent the graph

Answer 1

y ≤ 2.5x-3

Explanation:

we know two points: (2 , 2 ) and ( 0 , -3)

`Grad = (2--3)/(2-0) =(5)/(2) =2.5\\`

we also know the y intercept is -3

therefore equation in question is :
`y = 2.5x-3`

we take any point either above the line or below the line and substitute in the equation above. Let us try point (0,0) which is above the line and in the unwanted(shaded region):

y = 2.5x-3

0=2.5(0)-3

0=-3

Normally 0 can never be equal to -3 but is ≥ -3.

Since the point taken was not in the wanted region we reverse ≥ to ≤ to show the wanted region. The inequality in question becomes :

y ≤ 2.5x-3

Answer 2

y > 5/2x - 3

Find slope using (difference in y/ difference in x) of the two points (5/2)
y-intercept given (-3)
y is greater than because the shaded region is above the dotted line