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assuming that this relationship is linear, write an equation of the form p= mx+b that relates the price to the number of recliners sold

assuming that this relationship is linear, write an equation of the form p= mx+b that-example-1

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Answer: p = (-1/3)x + 700

Explanation:

To find the equation of the line that relates the price of the recliners to the number sold, we need to use the two given data points: (p=300, x=600) and (p=275, x=675).

We know that the equation of a line in slope-intercept form is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept. The slope formula is (y2-y1)/(x2-x1).

In this case, the dependent variable is the price (p) and the independent variable is the number of recliners sold (x). So we want to find the equation p = mx + b.

First, we need to find the slope (m) of the line. The slope is given by:

m = (change in p) / (change in x)

m = (275 - 300) / (675 - 600)

m = -25 / 75

m = -1/3

Next, we can use one of the given data points and the slope to find the y-intercept (b) of the line. Let's use the point (300, 600):

600 = (-1/3) * 300 + b

600 = -100 + b

b = 700

Therefore, the equation that relates the price of the recliners to the number sold is:

p = (-1/3)x + 700.

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