Question

Between 1990 and 1999, the number of movie screens in the United States increased by about 1500 each year. In 1996, there were 29,690 movie screens. Write an equation of a line, in slope-intercept form, to find the total number of screens y for any year x.

Answer 1

How far did you get with this?

Answer 2

\(\color{#0cbb34}{\text{Originally Posted by}}\) @jimthompson5910
How far did you get with this?
\(\color{#0cbb34}{\text{End of Quote}}\)
NO where i am stumped on this

Answer 3

The portion that says "increased by about 1500 each year" indicates the slope is m = 1500
This is because the slope represents the rate of change.

Agreed or no?

Answer 4

Ok I agree

Answer 5

Also, the info that "In 1996, there were 29,690 movie screens" indicates x = 6 and y = 29690 pair up together. The x value represents the number of years after 1990.

Using x = 6, y = 29690, and m = 1500, we can solve for b in the equation below
y = mx+b
29690 = 1500*6+b

What do you get when you solve for b?

Answer 6

ok give me a sec let me work that out

Answer 7

\(\color{#0cbb34}{\text{Originally Posted by}}\) @jimthompson5910
Also, the info that "In 1996, there were 29,690 movie screens" indicates x = 6 and y = 29690 pair up together. The x value represents the number of years after 1990.

Using x = 6, y = 29690, and m = 1500, we can solve for b in the equation below
y = mx+b
29690 = 1500*6+b

What do you get when you solve for b?
\(\color{#0cbb34}{\text{End of Quote}}\)
where did 6 come from?

Answer 8

1996 is 6 years after 1990, so x = 6 represents this

Answer 9

\(\color{#0cbb34}{\text{Originally Posted by}}\) @jimthompson5910
1996 is 6 years after 1990, so x = 6 represents this
\(\color{#0cbb34}{\text{End of Quote}}\)
oh ok thxs

Answer 10

no problem

Answer 11

i'm almost done with solving

Answer 12

alright

Answer 13

I don't think this is right. Ok I did 1500 divide 29690 which I got 0.050 then I brought the 6+b which I made 6b, so I divided 6 and 0.050 then got the answer b=0.0083

Answer 14

What do you get when you evaluate 1500*6

Answer 15

wait ok yeah I didn't work that out right hold on i'm sorry thank you for helping me out

Answer 16

no worries

Answer 17

Ok now I got 9000 when I did 6*1500

Answer 18

correct, so we go from
29690 = 1500*6+b
to
29690 = 9000+b

This is the same as saying
29690 = b+9000

Answer 19

How can we undo that "plus 9000"?

Answer 20

we would subtract 9000 from 29690 which then equals 20690 = b right?

Answer 21

yep so because b = 20690 we go from y = mx+b to y = 1500x+20690

The y intercept 20690 is the number of screens in 1990.
This is because x = 0 corresponds to the year 1990.

Answer 22

Ok that makes since now. Thank you so much jimthompson5910

Answer 23

You're welcome