Consider that a writer finishes a project that a coworker started at a rate of 3 pages per hour. We want to write an equation for the total number y of pages that have been finished after the writer works for x hours if the project is 200 pages long. To do so, let's recall the slope-intercept form of a linear equation.
y= mx+ b
Here, m is the slope and b is the y-intercept. In our case, x represents the working hours and y the number of pages. We are told that after 3 hours the 25 percent of the project is complete. Then, the sum of the pages written by the coworker and the writer after 3 hours will be equal to the 25 percent of 200.
b+9=0.25(200)
Notice that the number of pages finished by the writer is equal to 9. This is because the writer finishes 3 pages per hour, then after 3 hours the writer finishes 9 pages. The value b represents the number of finished pages before the writer started working on the project. Let's solve this equation for b.
This represents the number of pages written by the coworker. Since the slope represents the ratio between the change of two variables, the slope for our situation will be the number of pages per hour. Then, m= 3. The y-intercept occurs when x=0. In our case, it represents the quantity of pages written before the writer working begins.
y= 3x+ 41
To graph this, we will evaluate the given equation for 1, 3, and 5. Let's do it!
x
y=3x+41
y
3
y=3( 3)+41
50
8
y=3( 10)+41
65
13
y=3( 13)+41
80
Let's plot these points in a coordinate plane and connect them with a line to obtain the graph of the equation.
We are told that the writer has a total of 45 hours to finish the project. Let's find the amount of pages that the writer can complete in 45 hours by using the equation obtained in Part A.
y=3x+41
We can substitute x= 45 into the above equation to calculate the number of pages.
