Question

A car salesman earns a yearly salary plus commission for every car he sells. Last year, he sold 7 cars and made a total of $44,700. This year he sold 11 cars and made $46,800. Let x represent the number of cars he sells and y represent the total amount he makes a year. Write the slope-intercept equation that models the situation.

Answer 1

The car salesman's earnings can be modeled by the linear equation y = $525x + $41,025, where x is the number of cars sold, and y is the total earnings.

Step-by-step explanation:

To model the car salesman's earnings with a linear equation, we start with two given points: (7, $44,700) and (11, $46,800). Here, x represents the number of cars sold, and y represents the total earnings. To find the slope (m), we use the formula m = (y2 - y1) / (x2 - x1). This gives us:

m = ($46,800 - $44,700) / (11 - 7) = $2,100 / 4 = $525.

The slope of $525 represents the commission earned per car sold. Now, we can use one of the points to find the y-intercept (b) by rearranging the slope-intercept form equation: y = mx + b. Substituting x = 7 and y = $44,700 gives us:

$44,700 = $525(7) + b

$44,700 = $3,675 + b

b = $44,700 - $3,675 = $41,025.

Finally, the slope-intercept equation that models the salesman's earnings is:

y = $525x + $41,025