Need Help with Point-Slope form

Question

The math department sponsors a Math Family Fun Night each year. In the first year, there were 35 participants. In the third year, there were 57 participants.

• Write an equation to predict how many participants at any given year.

•  How many participants are predicted for the 5th year?

 

Answer 1

 

years on x axis

no.of participant on y axis

 

 year(x),          no. of participant(y)

 

For first year  order pair as (1,35)

for third year order pair is(3,57)

 

so slope=m =( y2-y1 ) /(x2-x1)=(57-35)/(3-1)=11

 

point slope form is

 

y-y1=m(x-x1)

 

we can consider any 1 point as(x1,y1). So here  we consider (1,35)

 

y-35=11(x-1)  equation  in point slop form

 

y-35=11x-11

 

y = 11x + 24  equation in slope intercept form

 

 

Now How many participants are predicted for the 5th year?
 so x= 5

y=11(5)+24=55+24=79

 

 

Answer 2

1,35     3,57

 

slope = (57 - 35)/(3 - 1) = 11

 

y = 11 x + b

 

35 = 11 (1) + b

b= 24

 

y = 11x + 24

 

y = 11(5) + 24 = 79