Question

I just need the 4 blank spaces

Answer 1

Option D is correct.

3x - y ≥ 9

The graph is solid, so we can eliminate option B

x-intercept = 3

y-intercept = -9

The graph is the solution for option D

Step-by-step explanation

When plotting the graph of linear inequality equations, the first step is to first plot the graph of the straight line normally, using intercepts to generate two points on the linear graph.

If the inequality sign is (< or >), then the line drawn will be a broken line.

If the inequality sign is (≤ or ≥), then the line drawn is an unbroken one.

The shaded region now depends on whether the inequality sign is facing y or not.

If the inequality sign is facing y, it means numbers above the line plotted are the wanted region and the upper part of the graph is shaded.

If the inequality sign is not facing y, it means numbers below the line plotted are the wanted region and the lower part of the graph is shaded.

For this question, we can see that the line is unbroken, so, the inequality sign is (≤ or ≥).

We can then write the equation of this line.

The slope and y-intercept form of the equation of a straight line is given as

y = mx + b

where

y = y-coordinate of a point on the line.

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

b = y-intercept of the line.

So, we can compute the slope and y-intercept.

For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as

`Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=(y_2-y_1)/(x_2-x_1)`

For this question,

(x₁, y₁) and (x₂, y₂) are (0, -9) and (3, 0)

`\text{Slope = }(0-(-9))/(3-0)=(0+9)/(3)=(9)/(3)=3`

y-intercept is where the line crosses the y-axis and this occurs at y = -9

b = -9

y = mx + b

m = 3

b = -9

y = 3x - 9

Then, we can see that the area under the line is shaded, hence, the inequality sign will be ≤

y ≤ 3x - 9

-3x + y ≤ -9

Multiplying both sides by -1

3x - y ≥ 9

Hope this Helps!!!