Question

Which of the following inequalities matches the graph? graph of an inequality with a dashed line through the points (0, 7) and (1, 5) with shading below the line 2x + y < 7 2x − y > 7 2x + y < −7 The correct inequality is not listed

Answer 1

2x + y < 7

Step-by-step explanation:

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

Using our points, we have

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

Answer 2

2x + y < 7

Explanation:

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

`m=(y_2-y_1)/(x_2-x_1)`

Using our points, we have

`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