Question

Please please help me with this

Answer 1

Answer:

Step-by-step 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

$y=\frac{1}{2}x+1$

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

$y\leq \frac{1}{2}x+1$

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

$-\frac{1}{2}x+y\leq 1$

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:

$\frac{1}{2}x-y\geq -1$

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

$y=\frac{3}{2}x-3$ 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:

$y\geq \frac{3}{2}x-3$

In standard form:

$-\frac{3}{2}x+y\geq -3$ and not leading with a negative gives us

$\frac{3}{2}x-y\leq 3$

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