# 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?

Jan 8, 2018

The slope is $3$ and after $5$ weeks, Gavin will have $27. #### Explanation: If you plot a graph with money ($) on the $y$-axis and time (weeks) on the $x$-axis, you can see that the slope of the graph, or rise over run, is $3$.

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

$y = 3 x + 12$

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

$y = 3 \cdot 5 + 12$

$= 15 + 12 = 27$

Jan 8, 2018

Given standardised form $y = m x + c$
Slope is m=$3 y-intercept ->c=$12
After 5 weeks (x=5), " we have "y= $27 #### Explanation: Your starting point in the account is $12

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

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

$y = m x + 12$

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

$y = 3 x + c$

Now all we have to do is assign the count of weeks to $t$. The question askes for 5 weeks. So we make $\textcolor{red}{x = 5}$ giving:

$\textcolor{g r e e n}{y = m \textcolor{red}{x} + c \textcolor{w h i t e}{\text{ddd") ->color(white)("ddd}} y = 3 \left(\textcolor{red}{5}\right) + 12 = 27}$
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$\textcolor{b l u e}{\text{The slop } \to m = 3 \to}$ for every 1 along it goes up 3

$\textcolor{b l u e}{\text{y-intercept } \to c = 12 \to}$ y-axis crosses the x-axis at $x = 0$