Given the two points (-24,7) and (30,25) a. what is an equation passing through the points? b. is (51, 33) also on the same line? explain your reasoning)

Part 1) Given the two points (-24,7) and (30,25) a. What is an equation passing through the points?

step 1
find the slope m
m=(y2-y1)/(x2-x1)---->m=(25-7)/(30+24)----> m=18/54----> m=1/3

step 2
wit m=1/3 and the point (30,25)
find the equation of the line
y-y1=m*(x-x1)-----> y-25=(1/3)*(x-30)--->y=(1/3)*x-10+25
y=(1/3)*x+15

the answer Part 1) is
y=(1/3)*x+15

Part 2) Is (51, 33) also on the same line?
if the point (51.33) is on the line y=(1/3)*x+15
then
for x=51 the value of y must be 33
for x=51
y=(1/3)*51+15----> y=17+15----> y=32
32 is not 33 
so
the point does not belong to the given line

the answer Part 2) is
the point does not belong to the given line

see the attached figure

Yes i could be the length of the triangle