Question

Task 1 Table and Equation

Mo has $90.00 already saved and has a job making $8.00 per hour.

Fill in the table of values for Mo’s financial story

Time worked in Hours
0
1
2
3
4
5
6
Money Saved in Dollars
90
98
106
114
122
130
138


What is the slope (rate of change) for Mo?

What is the y intercept (starting point) for Mo?

Put that information together and write the slope intercept equation that models Mo’s story. Define your variables and write the function for Money Saved as a function of Time


Task 2 Solve for an Unknown
Mo wants to save enough to buy airpods for $130 How many hours must they work to save enough dollars for that purchase? Handwrite or type your solution to this problem, starting with your equation from Task 1, substituting in the goal value of $130, showing all inverse operation steps and ending with your answer in the correct units.

Answer 1

Mo's slope, or rate of change, is $8 per hour, and the y-intercept, or starting point, is $90. The slope-intercept equation modeling Mo's financial story is y = 8x + 90. Mo must work 5 hours to buy the airpods at $130.

Step-by-step explanation:

Task 1: Slope Intercept Equation

The slope (rate of change) for Mo represents how much money Mo saves per hour of work.

To find this, take two points from the table, for example, (0, 90) and (1, 98). The slope is the change in money saved ($98 - $90) divided by the change in hours worked (1 - 0), which is $8 per hour.

The y-intercept represents Mo's starting point, which is how much money Mo had before starting the job. In this table, it is clear that at time 0, Mo already has $90 saved, so the y-intercept is $90.

We define the variables as follows: Let y represent the Money Saved in Dollars, and let x represent the Time worked in Hours. Thus, the slope-intercept equation that models Mo’s story is y = 8x + 90.

Task 2: Solve for an Unknown

Mo wants to save $130. From the equation y = 8x + 90, we substitute the goal value for y:
130 = 8x + 90. To solve for x, we perform inverse operations:
130 - 90 = 8x
40 = 8x
x = 40 / 8
x = 5.

Therefore, Mo must work 5 hours to save enough dollars to buy the airpods.