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
[tex]y=\frac{1}{2}x+1[/tex]
Since the shading is below the line, the inequality sign is less than or equal to. The inequality, then, is
[tex]y\leq \frac{1}{2}x+1[/tex]
But the solutions are in standard form, so let's do that:
[tex]-\frac{1}{2}x+y\leq 1[/tex]
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:
[tex]\frac{1}{2}x-y\geq -1[/tex]
Let's do the sae with the lower line. The equation, in slope-intercept form is
[tex]y=\frac{3}{2}x-3[/tex] 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:
[tex]y\geq \frac{3}{2}x-3[/tex]
In standard form:
[tex]-\frac{3}{2}x+y\geq -3[/tex] and not leading with a negative gives us
[tex]\frac{3}{2}x-y\leq 3[/tex]
Those 2 solutions are in choice B, I do believe.
