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

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

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

so

The equation in slope intercept form is equal to

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

so

step 2

Find the inequality of the second line

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

The slope is

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

so

The equation in slope intercept form is equal to

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

so

Rewrite

----->  

therefore

The system of inequalities is

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."