What is the equation of the line that is parallel to the given line and passes through the point (12, −2)? a. y = -6/5x + 10 b. y = -6/5x + 12 c. y = –5/6x – 10 d. y = 5/6x – 12

D. y = 5/6x – 12

Step-by-step explanation:

Our first step is to determine the slope of the given line.  As we move from (0, -4) to (12, 6), x increases by 12 and y increases by 10.  Thus, the slope is

m = rise/run = 10/12, or m = 5/6.

Answer option D is the only one that has the same slope.  Thus, D is the answer.

- "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."