The table of values below represents a linear function and shows the amount of money in Juanita's savings account since she began her part-time job. What is her monthly rate of savings?
| Number of Months Working at Part-Time Job | 0 | 2 | 4 | 6 | 8 |
| :--------------------------------------- | :-- | :-- | :-- | :-- | :-- |
| Amount in Saving Account (in dollars) | $36 | $60 | $84 | $108 | $132 |
A. $12 per month
B. $18 per month
C. $24 per month
D. $36 per month
Answer (1)
Calculate the slope using points (0, 36) and (2, 60): m = 2 − 0 60 − 36 .
Simplify the expression: m = 2 24 .
Calculate the slope: m = 12 .
Juanita's monthly rate of savings is $12 per month.
Explanation
Understanding the Problem We are given a table of values representing a linear function that shows the amount of money in Juanita's savings account since she started her part-time job. We need to find her monthly rate of savings. The monthly rate of savings is the slope of the linear function.
Finding the Slope To find the slope, we can use any two points from the table. Let's use the points (0, 36) and (2, 60). The slope, m , is given by the formula: m = x 2 − x 1 y 2 − y 1 where ( x 1 , y 1 ) and ( x 2 , y 2 ) are the coordinates of the two points.
Calculating the Slope Plugging in the values, we get: m = 2 − 0 60 − 36 = 2 24 = 12 So, the slope is 12.
Verifying the Slope Alternatively, we can use the points (2, 60) and (4, 84). The slope, m , is given by the formula: m = x 2 − x 1 y 2 − y 1 Plugging in the values, we get: m = 4 − 2 84 − 60 = 2 24 = 12 So, the slope is still 12.
Determining the Monthly Rate of Savings The monthly rate of savings is the slope of the linear function, which we found to be $12. Therefore, Juanita's monthly rate of savings is $12 per month.
Examples
Understanding the rate of savings is crucial for financial planning. For example, if Juanita wants to save for a $1200 laptop, knowing her monthly savings rate of $12 helps her calculate that it will take her 100 months (1200 / 12 = 100) to save enough money. This kind of calculation is essential for setting financial goals and making informed decisions about spending and saving.
