Question

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?

Answer 1

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 = 3x + 12`

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

`y = 3*5 +12`

`= 15 + 12 = 27`

Answer 2

Given standardised form `y=mx+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=mx+c`

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

`y=mx+12`

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

`y=3x+c`

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

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

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