Question

Which system of linear inequalities is represented by the graph? y > One-thirdx + 3 and 3x – y > 2 y > One-halfx + 3 and 3x – y > 2 y > One-thirdx + 3 and 3x + y > 2 y > One-thirdx + 3 and 2x – y > 2

Answer 1

Answer:

$y\geq \frac{1}{3}x+3$

$3x-y>2$

Step-by-step explanation:

The complete question is

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, 3) and (3, 4). Everything above the line is shaded. The second dashed line has a positive slope and goes through (0, negative 2) and (1, 1). Everything to the right of the line is shaded. Which system of linear inequalities is represented by the graph?

step 1

Find the inequality of the first solid line

we have the points (0,3) and (3,4)

The slope is

$m=(4-3)/(3-0)=\frac{1}{3}$

The y-intercept is the point (0,3)

so

The equation in slope intercept form is equal to

$y=\frac{1}{3}x+3$

Remember that everything above the line is shaded and is a solid line

so

$y\geq \frac{1}{3}x+3$

step 2

Find the inequality of the second line

we have the points (0,-2) and (1,1)

The slope is

$m=(1+2)/(1-0)=3$

The y-intercept is the point (0,-2)

so

The equation in slope intercept form is equal to

$y=3x-2$

Remember that everything to the right of the line is shaded and is a dashed line

so

$y$

Rewrite

$2$ ----->  $3x-y>2$

therefore

The system of inequalities is

$y\geq \frac{1}{3}x+3$

$3x-y>2$

Answer 2

Answer:

Which system of linear inequalities is represented by the graph?

A.

y > One-thirdx + 3 and 3x – y > 2

Step-by-step explanation: