Write the point slope form of the line that passes through (-8,2) and is parallel to a line with a slope of -8. include all your work in your answer.

The point slope form of the line that passes through (-8,2) and is parallel to a line with a slope of -8 is 8x + y + 62 = 0

Solution:

The point slope form of the line that passes through the points and parallel to the line with slope “m” is given as  

--- eqn 1

Where “m” is the slope of the line.  

are the points that passes through the line.

From question, given that slope “m” = -8

Given that the line passes through the points (-8,2).Hence we get

By substituting the values in eqn 1, we get the point slope form of the line which is parallel to the line having slope -8 can be found out.

y-2=-8(x-(-8))

On simplifying we get

y – 2 = -8(x +8)

y – 2 = -8x -64

y – 2 +8x +64 = 0

8x + y +62 = 0

Hence the point slope form of given line is 8x + y +62 = 0

- "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."

look at photo