what steps would I take to solve this and graph it?
Hi Jen;
-3x+4y=8
To convert this into a graphing equation, we must use the format of...
y=mx+b
m=slope
b=y-intercept
-3x+4y=8
Let's isolate y.
We will begin by adding 3x to both sides...
3x-3x+4y=8+3x
4y=8+3x
or
4y=3x+8
We will now divide both sides by four...
(4y)/4=((3x)/4)+8/4
Simplify...
y=((3/4)(x))+2
The slope of the line is 3/4...
Slope= (y_{2}-y_{1})/(x_{2}-x_{1})
This means that as the y-coordinators change by 3 units, the x=coordinates change by 4.
Let's plug in a few numbers...
x=4-------y=((3/4)(4))+2=3+2=5
x=8-------y=((3/4)(8))+2=6+2=8
x=12----y=((3/4)(12))+2=9+2=11
The y-intercept is the position of y when x=0...
y=(3/4x)+2
y=((3/4)(0))+2
y=2
(0,2) is the y-intercept.