Question

Which system of inequalities does the graph represent? Which test point satisfies both of the inequalities in that system?

Answer 1

Answer:

1) The inequality for the given system are

y ≥ 4x - 4

y ≥ x - 1.5

2)  The test point (0,0)  satisfies both of the inequalities in the system represented by the graph.

Step-by-step explanation:

Given : A graph showing  a system of inequalities.

We have to find the system of inequality.

For line 1)

The points that cut the x and y axis are (1,0) and (0,-4)

Thus, we can find the equation of line using two given point.

Since the general equation of line is y = mx + c

Where m is slope and c is y intercept

Slope is find as $m=\frac{y_2-y_1}{x_2-x_1}$

Substitute, we get,

$m=\frac{-4-0}{0-1}=4$

Slope is 4.

Thus, equation becomes y = 4x + c

For c put (0,-4)  in the above equation , we have,

-4 = 4(0) + c ⇒ c = -4

Thus, equation becomes y = 4x - 4

For inequality take a test point (0,0) and we check for which inequality it satisfies the graph region

For (0,0)

y = 4x - 4 becomes 0 = - 4  is satisfied when 0 > -4

thus, the inequality becomes y ≥ 4x - 4

Since, the line is a solid so it will take up equality sign too.

For line 2)

The points that cut the x and y axis are (1.5,0) and (0,-1.5)

Thus, we can find the equation of line using two given point.

Since the general equation of line is y = mx + c

Where m is slope and c is y intercept

Slope is find as $m=\frac{y_2-y_1}{x_2-x_1}$

Substitute, we get,

$m=\frac{-1.5-0}{0-1.5}=1$

Slope is 1.

Thus, equation becomes y = x + c

For c put (0,-1.5)  in the above equation , we have,

-1.5 = (0) + c ⇒ c = - 1.5

Thus, equation becomes y = x - 1.5

For inequality take a test point (0,0) and we check for which inequality it satisfies the graph region

For (0,0)

y = x - 1.5 becomes 0 = -1.5  is satisfied when 0 > - 1.5

thus, the inequality becomes y ≥ x - 1.5

Since, the line is a solid so it will take up equality sign too.

Thus, the inequality for the given system are

y ≥ 4x - 4

y ≥ x - 1.5

Also,  The test point (0,0)  satisfies both of the inequalities in the system represented by the graph.