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Solve the equation to set y = something. Remember the fundamental linear equation is y = mx + b.
Start with the initial equation:
3x - 5y = 8
Subtract 3x from both sides:
-5y = 8 - 3x = -3x + 8
Divide both sides by -5
y = -3x/-5 + 8/-5
Which looks like the following when formatted:
Now you just graph it:
We can check our graph by visually inspecting it.
It slopes up to the right, so the slope is positive.
Our 'm' term (the slope) is 3/5, which is right.
The y-intercept is -8/5 = -1.6, which is right.
The x-intercept is the value of x that makes y=0, which is right, too.