Question

On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, negative 1). Everything to the left of the line is shaded. Which linear inequality is represented by the graph? y > 2x + 3 y < 2x + 3 y > −2x + 3 y < −2x + 3

Answer 1

Explanation:

The Last one

Answer 2

Answer: Last option.

Explanation:

The equation of the line in Slope-Intercept form is:

`y=mx+b`

Where "m" is the slope of the line and "b" is the y-intercept.

The slope of a line can be found with this formula:

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

In this case, knowing that this line goes through the points (0,3) and (2,-1), you get that its slope is:

`m=(-1-3)/(2-0)\\\\m=-2`

By definition, a line intersects the y-axis when
`x=0`.

Since the line goes through the point (0,3), you can identify that:

`b=3`

Then, the equation of this line in Slope-Intercept form, is:

`y=-2x+3`

You know that everything to the left of the dashed line is shaded, then the symbol of the inequality is
`<`.

Therefore, the linear inequality that is represented by the graph is:

`y<-2x+3`