Question

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 $61, while 4000 shirts can be sold at a price of $45. Give a linear equation in the form p = mn +-b that gives the price p they can charge for n shirts.

Answer 1

The linear equation that represents the relationship between the number of shirts sold and the price is p = -0.008n + 77.

Step-by-step explanation:

To find the linear equation that represents the relationship between the number of shirts sold, n, and the price, p, we can use the given information to find the slope, m, and the y-intercept, b. First, we find the slope using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are points on the line. Substituting the values (2000, 61) and (4000, 45) into the formula, we get m = (45 - 61) / (4000 - 2000) = -0.008. Next, we find the y-intercept using the equation b = y - mx. Substituting the values (2000, 61) and m = -0.008 into the equation, we get b = 61 - (-0.008 * 2000) = 77. Therefore, the linear equation is p = -0.008n + 77.