Question

The mathematics department sponsors Math Family Fun Night every year. In year 1, there were 35 participants. In year 3, there were 57 participants. They determined that they could write an equation of a line using (1,35) and (3,57) as their two points. What equation of a line can the Math department use to predict the amount of participants, y, for any given year, x?
A. y=111x+24
B. y=11x−24
C. y=22x+35
D. y=11x+24

Answer 1

Simple Answer:

D.  y=11+24

Answer 2

The equation of a line:
$y=mx+b$

$(1,35) \\ x_1=1 \\ y_1=35 \\ \\ (3,57) \\ x_2=3 \\ y_2=57 \\ \\ m=\frac{y_2-y_1}{x_2-x_1}=\frac{57-35}{3-1}=\frac{22}{2}=11 \\ \Downarrow \\ y=11x+b \\ \hbox{plug the values of } x_1 \hbox{ and } y_1 \hbox{ into the equation:} \\ 35=11 \times 1 + b\\ 35=11+b \\ 35-11=b \\ b=24 \\ \\ \boxed{y=11x+24}$

The answer is D.