The graph below represents which system of inequalities?

graph of two infinite lines that intersect at a point. One line is dashed and goes through the points (0, 2) (negative 2, 0) and is shaded in below the line. The other line is dashed, and goes through the points (0, 6) (3, 0) and is shaded in below the line.

y < -2x + 6

y < x + 2

y less than or greater to -2x + 6

y less than or greater to x + 2

y < 2 over 3x - 2

y > 2x + 2

None of the above

One line is dashed and goes through the points (0, 2) (negative 2, 0), the answer is y less than or greater to x + 2
he other line is dashed, and goes through the points (0, 6) (3, 0), the answer is y less than or greater to -2x + 6

Answer Link

MsEHolt MsEHolt · Answer 2 · 2018-08-16T19:59:45-04:00

The correct answer is:

y < -2x + 6
; and y < x + 2

Explanation:

We first find the related line for each inequality. For the first line, we find the slope using the formula

\(m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-2}{-2-0}=\frac{-2}{-2}=1\)

The y-intercept is one of the points given to us, (0, 2). This makes the equation of the line y=x+2. Since the graph is shaded below and the line is dashed, this makes the inequality y<x+2.

For the second line, the slope is

\(m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-6}{3-0}=\frac{-6}{3}=-2\)

The y-intercept is one of the points given to us, (0, 6). This makes the equation of the line y=-2x+6. Since the graph is shaded below the line and the line is dashed, the inequality is y<-2x+6.