What is the equation of a line that passes through the point (8, 1) and is perpendicular to the line whose equation is y=−2/3x+5 ? enter your answer in the box.

y=3/2x - 11

Step-by-step explanation:

To write the equation of a line we must have a slope and a point. To find the slope, take the slope from the equation -2/3 and make the negative reciprocal of it. All perpendicular lines have negative reciprocal slopes between the two lines. The slope is 3/2.

Now that we have the slope, plug in the slope and choose one point to plug into the point slope formula. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form.  

(y-1)=3/2(x-8)  

y-1= 3/2x -12

y=3/2x - 11

answer: it's d

step-by-step explanation:

- "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."