Question

ILL MARK BRAINLIEST !!!!!


which system of linear inequalities is represented by the graph?
a) y ≥ 1/3x + 3 and 3x - y > 2
b) y ≥ 1/3x + 3 and 3x - y > 2
c) y ≥ 1/3x + 3 and 3x + y > 2
d) y ≥ 1/3x + 3 and 2x - y > 2

Answer 1

Answer:

A and B look identical, so perhaps there was a typo?

The equations are:

$y\geq1/3x+3$

$3x-y>2$

Step-by-step explanation:

To find the system of linear inequalities represented by the graph, we need to find the equation of each line.

Red Line:

To find the equation of the red line, we need to first find the slope and the y-intercept.

Let's pick two points from the red line. We can use (0, 3) and (3, 4).

The slope formula is:

$m=\frac{y_2-y_1}{x_2-x_1}$

Let (0, 3) be (x₁, y₁) and let's let (3, 4) be (x₂, y₂). So, our slope is:

$m=\frac{4-3}{3-0}$

Subtract:

$m=1/3$

So, our slope is 1/3.

Note that (0,3) is also our y-intercept. So, our y-intercept is y=3.

Now, we can use the slope-intercept form:

$y=mx+b$

Where m is the slope and b is the y-intercept.

Substitute 1/3 for m and 3 for b. This yields:

$y=1/3x+3$

Now, we need to determine which sign to use.

Note that the red line is not dotted, meaning we need "or equal to."

Also, note that the shaded region is above our line. In other words, y must be greater than our equation.

So, our sign is "greater than or equal to."

This, the red inequality is represented by the equation:

$y\geq1/3x+3$

Blue Line:

Again, let's first find the slope and the y-intercept.

We can use the points (0, -2) and (1,1). Let (0,-2) be (x₁, y₁) and let's let (1, 1) be (x₂, y₂). Substitute them into the slope formula:

$m=\frac{1-(-2)}{1-0}$

Evaluate:

$m=3/1=3$

So, our slope is 3.

(0, -2) is also our y-intercept. So, our y-intercept is y=-2.

Again, we can use the slope-intercept form:

$y=mx+b$

Substitute 3 for m and -2 for b:

$y=3x-2$

Now, we need to find our inequality sign.

Notice that the line is dotted. So, we won't have any "or equal to."

Also, notice that our shaded region is below our line. Thus, y is less than our equation. Therefore:

$y<3x-2$

However, all of our choices are in standard form. So, we need to convert this to standard form.

To do so, subtract 3x from both sides:

$-3x+y<-2$

The first term is traditionally positive. So, multiply both sides by -1. Since we're multiplying by a negative, flip the inequality sign:

$3x-y>2$

We can see that the answer choice that matches this is A (or B?)

And we're done!

Answer 2

Answer: A and B are identical so pick one of them

Step-by-step explanation: