To calculate the slope of the given function, find the rise and the run.
B
Substitute 640 for y into the linear function found in Part A.
A
y=40x+200
B
11
Practice makes perfect
We are asked to write a linear function that represents the total number of muffins the students will make y and the number of additional hours spent making the muffins x. 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, the eighth-graders can make 40 muffins in an hour. Therefore, the rise, or change in y, is 40 and the run, or change in x, is 1. We can substitute these values into the formula for the slope to calculate m.
m=40/1= 40
Next, we will find the y-intercept. Note that the eighth-graders have already made 200 muffins. Therefore, after 0 additional hours 200 muffins will be made. This means that b= 200. Now that we have the slope and the y-intercept we can write our final equation.
y= 40x+ 200
We are asked to find how many additional hours the students would spend to make 640 muffins. To do so, we will use the linear function that we found in Part A.
y=40 x+200This function represents the total number of muffins the student will make depending on the number of additional hours spent making the muffins x. Let's substitute 640 for y into the equation.
640=40 x+200
Now we will solve the obtained equation for x. Note that the value of x that satisfies the equation is the number of additional hours that the students would spend to make 640 muffins.
