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.