Algebra help?

Question

Find an equation of the line through (-1, 2) and (3, 10).
The answer is y= 2x+4, but I do not know how they got this. Help?

Answer 1

The usual way. First, find the slope (y goes up 8 when x goes up 4) so the slope is 2.
Then write the partially-solved equation line as
y = 2x + b.
Since (3,10) is on this line,
10 = 2(3) + b, so b=4.
YOU BETTER KNOW HOW THIS WORKS OR YOUR BUTT WILL BE SHREDDED IN TESTS.

Answer 2

first find the slope which is rise over run
the rise is from 2 to 10 which is 8 (10-2)
the run is -1 to 3 which is 4 (3- -1)
rise over run is 8/4 which is 2

in y = mx +b
m is the slope and is two for this equation (b is the y intercept)
so we have y = 2x +b
you already have two sets of y's and x's so we can plug in either one. for simplicity we'll use (-1,2)
2 = 2*-1 + b
2 = -2 +b
4 = b
plug it in
y = 2x + 4

to check put in the other x and y
10 = 2*3 +4
10 = 6 +4
10 = 10
check, it works

Answer 3

you could also use the two point form

(y-2) / (10-2) = (x- -1) / (3- -1)