Question

Write a system of linear inequalities to represent each graph

Answer 1

So since both of these lines are solid lines and not dashed, that means that the inequalities will have either ≤ or ≥.

Starting with the vertical line, since every point on that line is (0,y), this means that this line is x_0. And since the shaded region on this line is to the left of this line, this means that this inequality is x ≤ 0.

Now with this next line, I'll be forming it using the slope-intercept form (y = mx+b, m = slope and b = y-intercept). From looking at the graph, we can tell that the y-intercept is (-5,0). To find the slope, the equation is $\frac{y_2-y_1}{x_2-x_1}$ . For this, the two points I'll be using are (-4,-8) and (8,1).

Our equation will look and be solved like this: $\frac{1-(-8)}{8-(-4)}=\frac{9}{12} =\frac{3}{4}$

And since the region shaded is below the line, ≤ symbol will be used with our inequality.

Using the information above, our inequality is y ≤ 3/4x - 5.

In short, the system of inequalities is x ≤ 0 and y ≤ 3/4x - 5.