Exercise 12 Page 192

We are given an equation that represents the number of new vocabulary words y we learn after x weeks. y=15x We want to graph the equation and interpret the slope. First, we make a table of values with three solutions of the equation. Let's calculate the value of y when x is 1, 2, and 3.

x	y=15x	y	(x,y)
1	y=15( 1)	15	( 1, 15)
2	y=15( 2)	30	( 2, 30)
3	y=15( 3)	45	( 3, 45)

All the ordered pairs of the equation are points on its graph. Let's plot the points (1,15), (2,30), and (3,45) and draw a straight line between them to get our graph.

Next, we want to interpret the slope. Let's look at the graph and find out how y changes for every step x increases by 1.

We can see that y increases by 15 when x increases by 1. In our context, this means that we learn 15 new vocabulary words every week.

In this part, we want to determine how many new vocabulary words we learn after 5 weeks. We can substitute 5 for x in the given equation and evaluate for y. y=15 x ⇓ y=15( 5)=75 Another way to solve the exercise is to use the graph of the equation we made in Part A. Let's use it to check our answer!

We can see that our answer is correct. We learn 75 new vocabulary words after 5 weeks.

We want to know how many more vocabulary words we learn after 6 weeks than after 4 weeks. We have an equation that represents how many new vocabulary words y we learn after x weeks. y=15xLet's evaluate the value of y when x is 4 and 6. y=15( 4)= 60 y=15( 6)= 90 Now, we can calculate the difference between the two values of the number of words y. 90- 60=30 This means that we learn 30 more vocabulary words after 6 weeks than after 4 weeks.