Gavin has $12 in his savings account and adds $3 each week, how do you identify the slope, y-intercept and write the equation for the amount in your savings account? How much will Gavin have after 5 weeks?

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Gavin has $12 in his savings account and adds $3 each week, how do you identify the slope, y-intercept and write the equation for the amount in your savings account? How much will Gavin have after 5 weeks?

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Answer 1 · 2018-01-08T14:13:43

The slope is $3$ $3$ and after $5$ $5$ weeks, Gavin will have $$ 27$ $$27$ .

Explanation:

If you plot a graph with money $($)$ $($)$ on the $y$ $y$ -axis and time (weeks) on the $x$ $x$ -axis, you can see that the slope of the graph, or rise over run, is $3$ $3$ .

The $y$ $y$ -intercept is $12$ $12$ on the graph, so you get an equation:

$y = 3 x + 12$ $y = 3x + 12$

Since the time, $x$ $x$ , has been given as $5$ $5$ weeks, you can use it to find $y$ $y$ :

$y = 3 \cdot 5 + 12$ $y = 3*5 +12$

$= 15 + 12 = 27$ $= 15 + 12 = 27$

Answer 2 · 2018-01-08T14:47:03

Given standardised form $y = m x + c$ $y=mx+c$
Slope is $m = $ 3$ $m=$3$
y-intercept $\to c = $ 12$ $->c=$12$
After 5 weeks $(x = 5), we have y = $ 27$ $(x=5), " we have "y= $27$

Explanation:

Your starting point in the account is $$ 12$ $$12$

Now consider the standardised form of: $y = m x + c$ $y=mx+c$

$c$ $c$ is the value (starting point) when $x = 0$ $x=0$ so $c = 12$ $c=12$ giving:

$y = m x + 12$ $y=mx+12$

The rate of change for each week is $$ 3$ $$3$ so we set $m = $ 3$ $m=$3$ giving:

$y = 3 x + c$ $y=3x+c$

Now all we have to do is assign the count of weeks to $t$ $t$ . The question askes for 5 weeks. So we make $x = 5$ $color(red)(x=5)$ giving:

$y = m x + c ddd \to ddd y = 3 (5) + 12 = 27$ $color(green)(y=mcolor(red)(x)+c color(white)("ddd") ->color(white)("ddd")y=3(color(red)(5))+12 = 27)$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$The slop \to m = 3 \to$ $color(blue)("The slop "->m=3 ->)$ for every 1 along it goes up 3

$y-intercept \to c = 12 \to$ $color(blue)("y-intercept "->c=12->)$ y-axis crosses the x-axis at $x = 0$ $x=0$

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Gavin has $12 in his savings account and adds $3 each week, how do you identify the slope, y-intercept and write the equation for the amount in your savings account? How much will Gavin have after 5 weeks?

2 Answers

Explanation:

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