To find the slope, use any two points that lie on the line.
Graph:
Slope: 20 Interpretation of the Slope: See solution.
Practice makes perfect
We want to draw a graph of the homework problems completed versus time, find the value of the slope, and interpret it in words. Let's start by making a table to find the number of homework problems Zack completed after 0, 1, 2, 3, and 4 hours.
Time (hours)
0
1
2
3
4
Number of Homework Problems
We know that Zack completes 20 homework problems in 1 hour. Using this information, we can complete the table.
Time (hours)
0
1
2
3
4
Number of Homework Problems
20(0)=0
20(1)=20
20(2)=40
20(3)=60
20(4)=80
Let's write the two quantities as ordered pairs where the x-coordinate is the time and the y-coordinate is the number of homework problems Zack completed.
Finally, we will connect the ordered pairs and extend the line to the y-axis.
Next, we will find the slope of the line. Recall that we can calculate the slope of a line using the following formula.
Slope=Change in y/Change in x
Let's start by picking any two points on the line.
Now we can calculate the slope using the formula.
Slope=40-20/2-1= 20/1=20
We got that the slope is 20. The slope of the line is the rate at which the number of homework problems completed by Zack increases. Zack completes 10 additional homework problems every hour.
