To calculate the slope of the function, find the rise and the run.
B
To calculate the slope of the function, find the rise and the run.
A
y=6.5x+3.99
B
See solution.
Practice makes perfect
We are asked to write a linear function that represents the total cost y in dollars for a single order of x sweatshirts. The desired linear function has to follow a specific format.
y= mx+ b
For an equation in this form, m is the slope and b is the y-intercept. We will find the slope and the y-intercept one at time. Let's start by recalling that the definition of the slope of a linear function can be written in terms of rise and run.
m=rise/run
In this case, ordering one sweatshirt more increases the total cost by $ 6.50. Therefore, the rise, or change in y, is 6.5 and the run, or change in x, is 1. We can substitute these values into the formula for the slope to calculate m.
m=6.5/1= 6.5
Next, we will find the y-intercept. Note that no matter how many sweatshirts we order, we will pay a flat fee of $ 3.99. In particular, if we order 0 sweatshirts, the total cost will be $ 3.99. This means that b= 3.99. Now that we have the slope and the y-intercept we can write our final equation.
y= 6.5x+ 3.99
We are asked to describe how the linear function would change if the shipping charge applied to each sweatshirt. To do so, we will find the linear function that represents the new total cost y in dollars for a single order of x sweatshirts. The desired linear function has to follow a specific format.
y= mx+ b
For an equation in this form, m is the slope and b is the y-intercept. We will find the slope and the y-intercept one at time. Let's start by recalling that the definition of the slope of a linear function can be written in terms of rise and run.
m=rise/run
In this case, ordering one sweatshirt more increases the total cost by $ 6.50 and $3.99. Therefore, the rise, or change in y, is 6.50+3.99 and the run, or change in x, is 1. We can substitute these values into the formula for the slope to calculate m.
m=6.50+3.99/1= 10.49
Next we will find the y-intercept. This time, we pay for the shipping of each sweatshirt. This means that if we order 0 sweatshirts, the total cost will be $ 0. Therefore, b= 0. Now that we have the slope and the y-intercept we can write our final equation.
y= 10.49x+ 0 ⇔ y=10.49x
Note that the obtained linear function has a different slope and y-intercept than the function that we found in Part A.
