Sophia trains with her friend Aisha on a 5-kilometer trail near their school. Aisha starts running right after school and runs an average of one kilometer in seven minutes.
Sophia leaves 10 minutes later and runs at a steady pace shown in the table below.
Write each function as a linear equation where x is the number of kilometers and y is the number of minutes.
Who runs faster? Explain.

y = 7x

y = 5.5x

Sophia

Step-by-step explanation:

Given that:

Aisha runs 1 km in 7 minutes :

Aisha's function :

y = 7x

x = number of kilometers and y is the number of minutes

For Sophia :

Slope = change in y / change in x = (15.5 - 10) / (1 - 0)

Slope = 5.5

Hence, Sophia :

y = 5.5x

Hence, Sophia runs faster as she completes one kilometer in 5.5 minutes. Which is lesser Than Aisha's time. Of 7 minutes.

- "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."