Question

1. Which equation correctly represents the graph below? 30 27 24 21 15 12 6 1 2 3 4 5 6 7 8 9 10

Answer 1

the general equation of a line is

$y=mx+b$

where m is the slope and b the y-intercept

we can notice the y-intercept on the graph, is 12, because is the coordinate were x=0 or were the line touch the y-axis

now we need to find the slope, ussing

$m=\frac{y2-y1}{x2-x1}$

where (x2,y2) is a rigth point from (x1,y1), I can take any point of the line, for this case I will use (0,12) and (2,15)

where (2,15) is a right point from (0,12)

so, replacing

$\begin{gathered} m=\frac{15-12}{2-0} \\ \\ m=\frac{3}{2} \end{gathered}$

the slope is 3/2

now I can replace on the general equation ussing b=12 and m=3/2

$y=\frac{3}{2}x+12$