Question

Indicate in standard form the equation of the line passing through the given points.

R(3, 3), S(-6, -6)

Answer 1

you could use the xy formula, but i don't remember what that is exactly so let's get it from the standard equation of a line, that is, y=mx+b

Answer 2

we can solve for the slope with the two given points, knowing that it's rise over run, that's the change in y over the change in x

Answer 3

change in y would be 3-(-6)=9, change in x would be 3-(-6)=9, giving a slope of 9/9=1

Answer 4

great, so now we have y=mx+b, where m=1

Answer 5

from here we can plug in either point for x and y, and then solve for b

Answer 6

let's go with R (3, 3), because they're smaller numbers and they're positive! that makes them a bit easier, i think.

Answer 7

using R, we come out with (3)=(1)(3)+b

Answer 8

if we solve for b, we can get b=0. wonderful!

Answer 9

now we have values for m and for b that we can plug into the standard equation of a line, which is, remember, y=mx+b. plugging in our values, that leaves us with y=(1)x+(0), which we can simplify as just y=x! what a beautiful final answer, isn't it?