Question

Josie is saving money to purchase a new pair of shoes. She has already saved $5 and earn $0.50 for each chore she completes. Graph the relationship between number of chores Josie completes and the total amount she will have saved. What part of Josie's scenario represents the slope of the line you graphed? What part of Josie's scenario represents the y-intercept of the line you graphed?

Answer 1

From the given information, we can formulate the following expression:

Money saved = initial savings + earnings

We know that Josie initially had $5 and that she earns $0.5 per chore, then we can rewrite the above equation, like this:

Money saved = $5 + $0.5x

We can call "y" to the money saved:

y = 5 + 0.5x, in this case, x is the number of chores that she completes.

In this case, we have a linear equation, then its slope is the number that is multiplied by the independent variable "x" that is 0.5, in this scenario the slope represents the pay that she receives for each chore.

The y-intercept is the number that is being added to the 0.5x term, that is $5, it is the initial amount of money saved by Josie, then that's what the y-intercept represents in this scenario.

Graph

In order to graph a linear equation we just need to find two points of the graph, then we join them with the line, we can specify the points of the line by replacing some values of x and then calculating the corresponding value of y, like this:

• When x equals 0

y = 5 + 0.5*0

y = 5 + 0

y = 5

Then, one point of the line is located at (0,5)

• When x equals 18

y = 5 + 0.5*18

y = 5 + 9

y = 14

Then, another point of the line is located at (18,9)

Now we can graph the line as follows: