Line n has a slope of 5/3 and passes through the points (4p,-7) and (1,8). what is the value of p?

p =-2

Step-by-step explanation:

The slope is given by  

m = (y2-y1)/(x2-x1)

We have points (4p,-7) and (1,8) and the slope is 5/3

Substituting these in

5/3 = (8--7)/ (1-4p)

Simplifying

5/3 = (8+7)/ (1-4p)

Multiply by (1-4p) on both sides

5/3 (1-4p) = (15)/ (1-4p) * (1-4p)

5/3 (1-4p) = (15)

Multiply by 3 on both sides

5/3 *3(1-4p) = 3*(15)

5(1-4p) = 45

Distribute

5 - 20p = 45

Subtract 5 from each side

5-5-20p = 45-5

-20p = 40

Divide by -20

-20p/-20 = 40/-20

p =-2

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have