Question

elijah and aubrey have summer jobs. elijah deposits the same amount of money in his account every week. the equation y = 125x+72 represents his bank balance any given week of the summer. aubrey also deposits the same amount into her account every week. at the end of the third week she has $398. at the end of the sixth week she has $773. complete parts a to c below. a. (simplify your answer. type an equation. type your answer in slope - intercept form. use integers or decimals for any numbers in the equation.) y = 125x+23 b. would the graph of the equation for aubreys balance be parallel to the graph of elijahs balance? explain. the slopes of the lines are the same and the y - intercepts of the lines are different, so the lines are parallel. c. what do the parallel graphs mean in terms of the situation? elijah and aubrey each deposited $ each week. they started with different amounts in their accounts. elijah began with $ in his account, and aubrey began with $ in her account.

Explanation:

Step1: Find the slope - intercept form for Aubrey

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given Elijah's equation $y = 125x+72$. Since Aubrey's graph is parallel to Elijah's, they have the same slope. Let Aubrey's equation be $y = 125x + b$. We use the given points to find $b$. We know that when $x = 3$, $y=398$ and when $x = 6$, $y = 773$. First, substitute $x = 3$ and $y = 398$ into $y=125x + b$:
$398=125\times3 + b$
$398 = 375+b$

Step2: Solve for $b$

Subtract 375 from both sides of the equation:
$b=398 - 375=23$
So Aubrey's equation is $y = 125x+23$.

Step3: Interpret parallel lines in context

Parallel lines in the context of their bank - balance situation mean that Elijah and Aubrey save the same amount of money per week (the slope represents the weekly deposit amount), but they started with different initial amounts (the y - intercepts represent the starting balances).

Answer:

b. Aubrey's equation: $y = 125x + 23$. Parallel lines mean they save the same amount per week but started with different initial amounts.
c. The slopes being the same means they deposit the same amount of money each week. The different y - intercepts mean they started with different amounts of money in their accounts at the beginning of the summer.