Question

Please help i will give 20 points for both answers

Answer 1

1.) A

2.) D

Explanation:

1.) find equation of line:

b=3, m=1.5

y=1.5x+3

shaded is below therefore

y
`\leq`1.5x+3

*line under inequality because line is solid

2.) (1,5) is not a solution because it is above shaded figure

Answer 2

1. A -
`y\leq (3)/(2) x+3`

2. D - (1,5)

Explanation:

The equation
`y\leq (3)/(2) x+3` fits this graph.

y has to be less than x due to the shaded part of the graph being on the underside of the line

To confirm this we can plug in a value to see if the inequality is true

I will use the origin as an example:

`0\leq (3)/(2) (0)+3`

`0\leq 3`

This inequality is true meaning this point is in the shaded region of the graph

Also the equation has to have an equal to because it has a solid line and not a dotted line

The point that isn't a solution is (1,5) due to the fact it isn't in the shaded region and when plugged into the equation gives a false inequality

`5\leq (3)/(2) (1)+3`

`5\leq (3)/(2)+3`

`(10)/(2) \leq (9)/(2)`

This inequality is false which means the point (1,5) isn't a solution to this equation.