Remember that x represents the time that we spend assembling a birdhouse and y is the time we spend writing a paper.
A
Graph:
Interpretation: See solution.
B
20 minutes, see solution.
Practice makes perfect
We complete two projects for a class in 60 minutes. The given equation represents this situation.
x+y=60
Here, x represents the time that we spend assembling a birdhouse and y is the time we spend writing a paper. To graph this equation, we will start by finding the y-intercept. Remember that the y-intercept of a line is the y-coordinate of the point where the line crosses the y-axis. This will occur when x=0.
The y-intercept is equal to 60, which means that one point on the line is (0,60). Now we will find the x-intercept. Recall that the x-intercept is the x-coordinate of the point where the line crosses the x-axis. It occurs when y=0.
This means that another point on the line is (60,0). Let's plot the points in a coordinate plane and connect them with a line to obtain the graph of the given equation.
The y-intercept represents the time we spend writing a paper without assembling the bird house, and the x-intercept shows the time spent assembling the birdhouse without writing the paper.
We want to find the time we spend writing the paper if we spent twice as much time assembling the birdhouse as we do writing the paper. To do so, let's recall the given equation.
x+y=60
Here, x represents the time that we spend assembling a birdhouse and y is the time we spend writing a paper. Since we spend twice as much time assembling the birdhouse, we can substitute x= 2y into the above equation and solve it for y.
This means that we spend 20 minutes writing the paper.
Checking Our Answer
Checking our answer
To check our answer, we can use the obtained graph in Part A.
Remember that x represents the time that we spend assembling a birdhouse and y is the time we spend writing a paper. Then, we can identify the corresponding value of x for y=20 to obtain the value assembling a birdhouse.
This means that if we spend 20 minutes writing a paper, we need to spend 40 minutes assembling the birdhouse. Notice that 40 is the double of 20. 2(20)=40
Therefore, our answer is correct.
