Question

Please please help me with this

Answer 1

Explanation:

First find the equations of the lines, then fill in the proper inequality sign. The upper line has a y-intercept of 1 and a slope of 1/2, so the equation, in slope-intercept form is

`y=(1)/(2)x+1`

Since the shading is below the line, the inequality sign is less than or equal to. The inequality, then, is

`y\leq (1)/(2)x+1`

But the solutions are in standard form, so let's do that:

`-(1)/(2)x+y\leq  1`

AND they do not like to lead with negatives, apparently, so let's change the signs and the way the inequality is facing, as well:

`(1)/(2)x-y\geq  -1`

Let's do the sae with the lower line. The equation, in slope-intercept form is

`y=(3)/(2)x-3` since the slope is 3/2 and the y-intercept is -3. Now, since the shading is above the line, the inequality is greater than or equal to:

`y\geq (3)/(2)x-3`

In standard form:

`-(3)/(2)x+y\geq  -3` and not leading with a negative gives us

`(3)/(2)x-y\leq  3`

Those 2 solutions are in choice B, I do believe.