I really need help! A clothing business finds there is a linear relationship between the number of shirts,
n, it can sell and the price, p, it can charge per shirt. In particular, historical data shows that 2000 shirts can be sold at a price of $91, while 5000 shirts can be sold at a price of $82. Give a linear equation in the form p=mn+b that gives the price p they can charge for n shirts.

n = (-1000/3)p + (97000)/3)

Step-by-step explanation:

The data given says, in effect, that the linear equation based on price passes through 2 points (82, 5000) and (91, 2000), given two points on a line, we'll use the point-slope form to start.  To use this we must first find the slope

m = (y2 - y1) / (x2 - x1) = (2000 - 5000) / (91 - 82) = -3000 / 9 = -1000/3

(I like to leave slopes as fractions <rather than decimal> since fractions are more accurate)

point-slope form

y - y0 = m(x - x0) at some point (x0, y0) with slope m, we'll use (91, 2000)

y - 2000 = (-1000/3)(x - 91), distribute

y - 2000 = (-1000/3)x + 91000/3, add 2000 to each side

y = (-1000/3)x +97000/3

oops, substitute p for x and n for y

n = (-1000/3)p + (97000)/3)

positive

step-by-step explanation:

the quadrant is facing upwards