Question

Zachary purchased a computer for ​$1600 on a payment plan. Months after he purchased the​ computer, his balance was ​$850. Months after he purchased the​ computer, his balance was ​$350. What is an equation that models the balance y after x​ months? Write in slope-intercept form.

Answer 1

The equation that models the balance, y, after x months is y = -$187.5x + $1600 in slope-intercept form.

Step-by-step explanation:

The equation that models the balance, y, after x months can be written in slope-intercept form as:

y = mx + b

where m represents the slope of the line and b represents the y-intercept. To find the slope, we can use the formula:

m = (y2 - y1) / (x2 - x1)

In this case, we can choose two points on the line: (0, $1600) and (2, $850). Substituting these values into the slope formula:

m = ($850 - $1600) / (2 - 0) = -$375 / 2 = -$187.5

Now, we can substitute the slope, m, and one of the points into the slope-intercept form:

y = -$187.5x + b

Using the point (0, $1600) to find the y-intercept:

$1600 = -$187.5(0) + b

b = $1600

Therefore, the equation that models the balance, y, after x months is:

y = -$187.5x + $1600