Question

Write a system of linear inequalities to represent each graph

Please help with this graph asap, 12 points!

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.

Answer 2

Inequalities can be represented on graphs

The inequalities are: $\mathbf{x \le 0}$ and $\mathbf{y \ge \frac 57x + 7}$

The green graph is a vertical line that passes through the origin, and the left-hand side is shaded.

Also, the graph is a closed line.

So, the inequality is: $\mathbf{x \le 0}$

The blue graph passes through (0,-5) and (7,0)

Start by calculating the slope (m)

$\mathbf{m = \frac{0 --5}{7-0}}$

$\mathbf{m = \frac{5}{7}}$

The equation is then calculated as:

$\mathbf{y = m(x - x_1) + y_1}$

The right-hand side of the graph is shaded, and the line of the graph is a closed line.

So, the inequality is:

$\mathbf{y \ge m(x - x_1) + y_1}$

This gives

$\mathbf{y \ge \frac 57(x - 0) + 7}$

$\mathbf{y \ge \frac 57x + 7}$

Hence, the inequalities are: $\mathbf{x \le 0}$ and $\mathbf{y \ge \frac 57x + 7}$

Read more about inequalities at:

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