Question

tim explained a function in words and paul wrote an equation.
the amount of money in a savings account increases at a rate of $225 per month. after eight months, the bank account has $4,580 in it.
paul
y - 1,400 = 56(x + 26)
whose function has the smaller y - intercept?
○ tim’s with a y - intercept of $2,700
○ paul’s with a y - intercept of $2,856
○ paul’s with a y - intercept of $2,800
○ tim’s with a y - intercept of $2,780

Explanation:

Step1: Find Tim's y-intercept

Let $y$ = total amount, $x$ = months. The slope-intercept form is $y=mx+b$, where $b$ is the y-intercept. We know $m=225$, and when $x=8$, $y=4580$. Substitute into the formula:
$4580 = 225(8) + b$
$4580 = 1800 + b$
$b = 4580 - 1800 = 2780$

Step2: Find Paul's y-intercept

Rewrite Paul's equation into slope-intercept form ($y=mx+b$):
$y - 1400 = 56(x + 26)$
$y = 56x + 56(26) + 1400$
$y = 56x + 1456 + 1400$
$y = 56x + 2856$
Here, $b=2856$

Step3: Compare the two intercepts

Compare $2780$ (Tim's) and $2856$ (Paul's). $2780 < 2856$

Answer:

Tim's with a y-intercept of $2,780$