I need some help with this calculus question

The tangent to at the point (0, 5) has a slope equal to the derivative evaluated at .

This tangent passes through the point (0, 5), so its equation is

The normal line passes through the same point, but is perpendicular to the tangent line, so its slope is the negative reciprocal of the slope of the tangent. So the equation for the normal line 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."