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
Arushi M. ยท Stefan V.
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 = 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

Tony B
Jan 8, 2018

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)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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

Related questions
See all questions in Problem-Solving Models
Impact of this question
2700 views around the world
You can reuse this answer
Creative Commons License