Using the graph, find the slope and y-intercept of each line. Use them to write the equations in slope-intercept form.
B
b
What does the y-intercept represent? What does the slope represent?
A
a
Year 1: y=20x+20
Year 2: y=20x+60
B
b
Year 1:
Sign-up fee =$20
Membership cost =$20 Year 2:
Sign-up fee =$60
Membership cost =$20 Change in sign-up fee: $40 Change in membership cost: $0
Practice makes perfect
a
Let's write one equation at a time for each year.
Year 1
In order to write an equation in slope-intercept form, we need to know the slope and y-intercept. From the graph, we can see that the y-intercept is 20. Also, for each step to the right, the line goes 20 steps up. Therefore, the slope is 20. Let's substitute these values in the slope-intercept form of the equation.
We can write the equation for the second year in the same way. From the graph, we can tell that the y-intercept is 60. Notice, that the lines are parallel, which means that their slopes are the same. Therefore, the slope of the line is also 20. We can substitute these values into the slope-intercept form.
Let's think of what the slopes and y-intercepts could represent in the equations. We know that the sign-up fee is a one-time payment and it does not depend on time. Therefore, the y-intercept represents the cost of the sign-up fee. Using the equations from Part A, we can find the sign-up fees for each year.
Year $1$: $20
Year $2$: $60On the other hand, the membership fee is paid each month. In the equation, this value tells us the rate of the change. Therefore, the slope represents the membership cost.
Year $1$: $20
Year $2$: $20
As we can see, the monthly membership fees are the same for each year. Although, the sign-up fee in the second year is greater than in the first year. Let's calculate the difference.
60-20=$40
Therefore, the sign-up fee increased in the second year by $40 and the membership cost remained the same.
