graph question

I have a graph in front of me that has a line going through the y axis at -2 and the also hits the x axis at 6 ( i hope that explanation is understandable)

Which equation is the graph of?

x-3y=6
x+3y=6
3x-y=6
x-3y=-6

If I am thinking right I would plug the -2 in for y but they dont ever equal 6?

I have a graph in front of me that has a line going through the y axis at -2 and the also hits the x axis at 6 ( i hope that explanation is understandable)

Which equation is the graph of?

x-3y=6
x+3y=6
3x-y=6
x-3y=-6

If I am thinking right I would plug the -2 in for y but they dont ever equal 6?

1--The slope of the line is given by m = (y2-y1)/(x2-x1) = [0 -(-2)]/[6 - -0] = 1/3
2--Thr y intercept was given as -2.
3--Therefore, the line is defined by y = x/3 -2
4--At x = 0 y = -2 and when x = 6, y = 0.
5--At y = -2 x = 0 and when y = 0 y = -2.
6---2 = x/3 -2 or x/3 = 0 making x = 0.

Hello, boscothepug1!

I have a graph in front of me that has a line going through the y axis at -2 and the also hits the x axis at 6

Which equation is the graph?
\(\displaystyle \;\;\;x\,-\,3y\:=\:6\;\;\;x\,+\,3y\:=\:6\;\;\;3x\,-\,y\:=\:6\;\;\;x\,-\,3y\:=\:-6\)

If I am thinking right I would plug the -2 in for y but they dont ever equal 6?\(\displaystyle \;\) . . . of course not!

Click to expand...

You're plugging in \(\displaystyle y\,=\,-2\) and hoping to get \(\displaystyle x\,=\,6\)
You are insisting that \(\displaystyle (6,-2)\) is on the line . . . and it isn't!
\(\displaystyle \;\;\)(Look at the graph that's in front of you.)

You are given two points on the line: \(\displaystyle \,(0,\,-2)\) and \(\displaystyle (6,\,0)\)

\(\displaystyle \;\;\)and you're expected to write the equation of this line.