Question

Which of the following inequalities matches the graph?

-10-8-6-4-2
-2
-6
-8
O 2x-y> 7
O The correct inequality is not listed
O 2x+y<-7
O 2x+y<7
8 10

Answer 1

`2x + y < 7`

Explanation:

First we find the slope of the line that passes through the given points. The formula for slope is:

`\text{m}=(y_2-y_1)/(x_2-x_1)`

Using our points, we have

`\text{m}=(7-5)/(0-1) =(2)/(-1) =-2`

The y-intercept will be the point where the data crosses the y-axis. All y-intercepts have an x-coordinate of 0; since we already have the point (0, 7), we have the y-intercept at 7. This makes our equation

`y = -2x + 7`

The inequalities we're given are written in standard form, Ax+By=C. This means we need x and y on the same side of the equals in our equation.

Since the inequality is graphed below the line, we want our inequality to be

`y < -2x+7`

To move the x-value to the other side of the equation, we will add 2x to each side:

`y+2x < -2x+7+2x`

`y+2x < 7`

`2x+y < 7`