Question

Which of the following inequalities matches the graph? (1 point)

graph of an inequality with a dashed line through the points (0, 3) and (1, 9) with shading above the line


−6x + y < 3

6x + y < 3

6x − y < −3

The correct inequality is not listed

Answer 1

the correct answer is 6x − y < −3

Answer 2

`6x-y< -3`

The graph in the attached figure

Explanation:

Step 1

Find the equation of the line

we have

`A(0, 3), B(1, 9)`

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

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

substitute

`m=(9-3)/(1-0)`

`m=(6)/(1)=6`

The equation of the line into slope intercept form is equal to

`y=mx+b`

where

m is the slope

b is the y-intercept

In this problem we have

`m=6`

`b=3` ------> the y-intercept is the point B

substitute

`y=6x+3`

Step 2

Find the equation of the inequality

we know that

The solution is the shaded area above the dashed line

so

the inequality is equal to

`y>6x+3`

rewrite

`-6x+y>3` ------> multiply by
`-1` both sides

`6x-y< -3`

Step 3

Using a graphing tool

The x-intercept is the point
`(-0.5,0)`

The y-intercept is the point
`(0,3)`

The slope of the dashed line is positive

the graph in the attached figure