Question

Find an equation of the line passing through the pair of points. Write the equation in the form Ax+By = C.

(3,4) and (2,1)

Answer 1

y = 3x - 5

sorry can't help with step to step explanation......

Answer 2

-3x+y=-5

Explanation:

First, find the slope of the equation:

m=(y2-y1)/(x2-x1) ==> m=slope of equation

(x1, y1), (x2, y2) ==> (x1=3, y1=4), (x2=2, y2=1)

m=(1-4)/(2-3) ==> plugin x1=3, y1=4, x2=2, and y2=1

m=-3/(-1)

m=3

y=mx+b ==> slope-intercept equation

1=3(2)+b ==> plugin 3 for m and (2, 1) where x=2 and y=1

1=6+b ==> solve for b

1-6=6-6+b

b=-5

y=3x+(-5) ==> plugin -3 for m and -5 for b

y=3x-5 ==> simplify

Now, Isolate -5 since it is the only constant

y-3x=3x-3x-5 ==> isolate -5 by subtracting 3x on both sides

-3x+y=-5 ==> simplify and put in Ax+By=C form