tim explained a function in words and paul wrote an equation.\ntim\nthe amount of money in a savings account…

tim explained a function in words and paul wrote an equation.\ntim\nthe 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.\npaul\ny - 1,400 = 56(x + 26)\nwhose function has the smaller y - intercept?\ntims with a y - intercept of $2,700\npauls with a y - intercept of $2,856\npauls with a y - intercept of $2,800\ntims with a y - intercept of $2,780

tim explained a function in words and paul wrote an equation.\ntim\nthe 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.\npaul\ny - 1,400 = 56(x + 26)\nwhose function has the smaller y - intercept?\ntims with a y - intercept of $2,700\npauls with a y - intercept of $2,856\npauls with a y - intercept of $2,800\ntims with a y - intercept of $2,780

Answer

Explanation:

Step1: Find Tim's y - intercept

We know the slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. The slope $m = 225$ (rate of increase per month). After $x = 8$ months, $y=4580$. Substitute into $y=mx + b$: $4580=225\times8 + b$ $4580 = 1800 + b$ $b=4580 - 1800=2780$

Step2: Find Paul's y - intercept

Given the point - slope form $y - 1400=56(x + 26)$. Rewrite it in slope - intercept form $y=mx + b$. First, expand the right side: $y-1400=56x+56\times26$. $y-1400=56x + 1456$. Then, add 1400 to both sides: $y=56x+1456 + 1400=56x+2856$. So Paul's y - intercept is 2856.

Step3: Compare y - intercepts

Since $2780<2856$, Tim's function has the smaller y - intercept.

Answer:

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