Question

Carla is saving money for a trip this summer. She already has some money in her savings account and will add the same amount to her account each week. At the end of 2? weeks, Carla has? $130. At the end of 8? weeks, she has? $280. Write a linear function in the form y=mx+b to represent the amount of money m that Carla has saved after w weeks.

Answer 1

Y and x are not constants, so you don’t have to find the value of them.

On the other hand, you do have to find m and b. M is the slope and B is where the y-axis is crossed, or what her balance was at week 0.

To find slope: (y1-y2)/(x1-x2) or the rise over run.
130-280= -150
2-8= -6
-150/-6= 25= m
This means she adds $25 each week.

To find the y-intercept: this is where x=0 and y is some unknown value. We are given the amount at the end of 2 weeks, so we just need to go back 2 weeks. She adds $25 each week. -2 weeks • 25 = -$50
130-50= 80 = b, or the initial amount in the account.

We need to plug b and m into the equation.
y=25x+80