Question

emery borrowed money from her brother to buy a new phone and is paying off a fixed amount each week. after 2 weeks, she will owe $456, and after 5 weeks, she will owe $228.
a. what was the original amount emery borrowed?
b. how much does she pay each week?
c. how useful are equations in point - slope and slope - intercept forms for answering each question?
a. emery originally borrowed $608.
b. she pays $76 each week.
c. how useful are equations in point - slope and slope intercept forms for answering each question? select all that apply.
□a. the slope - intercept form can be used to find the original amount borrowed as the y - intercept.
□b. the point - slope form can be used to find the original amount borrowed as the y - intercept.
□c. the slope - intercept form can be used to find the amount she pays each week, which is the slope.
□d. the point - slope form can be used to find the amount she pays each week, which is the slope.

Explanation:

Step1: Find the amount paid per week

The change in the amount owed is $456 - 228=228$ dollars over a period of $5 - 2 = 3$ weeks. So the amount paid per week (slope) is $\frac{456 - 228}{5 - 2}=\frac{228}{3}=76$ dollars per week.

Step2: Find the original amount borrowed

Let $y$ be the amount owed and $x$ be the number of weeks passed. Using the point - slope form with the point $(2,456)$ and slope $m=- 76$ (negative because the amount owed is decreasing). The point - slope form is $y - y_1=m(x - x_1)$. So $y-456=-76(x - 2)$. Expanding gives $y-456=-76x + 152$. Then $y=-76x+608$. When $x = 0$ (original amount), $y = 608$.

Step3: Analyze the usefulness of forms

The slope - intercept form of a linear equation is $y=mx + b$ where $m$ is the slope (amount paid per week) and $b$ is the y - intercept (original amount borrowed). The point - slope form is $y - y_1=m(x - x_1)$ which can also be used to find the slope (amount paid per week) and by substituting $x = 0$ can find the original amount borrowed.

Answer:

a. $608$
b. $76$
c. A. The slope - intercept form can be used to find the original amount borrowed as the y - intercept.
C. The slope - intercept form can be used to find the amount she pays each week, which is the slope.
D. The point - slope form can be used to find the amount she pays each week, which is the slope.