SOLUTION: Find an equation in the form y=mx+b(where possible) for each line. through (2,-1), parallel to 3x-y=1

Algebra ->  Linear-equations -> SOLUTION: Find an equation in the form y=mx+b(where possible) for each line. through (2,-1), parallel to 3x-y=1       Log On


   

Question 127359: Find an equation in the form y=mx+b(where possible) for each line.
through (2,-1), parallel to 3x-y=1
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Lines are parallel if and only if their slopes are equal. So the first step is to find the slope of the given line by putting the equation into slope intercept form, i.e. solve for y:

3x-y=1

Add -3x to both sides:
-y=-3x%2B1

Multiply by -1:
y=3x-1

Now we know that the slope of the required line is 3 because the slope of the given line is 3.

Since we know the slope and one point of the required line, we can use the point-slope form of the line to derive the equation.

y-y%5B1%5D=m%28x-x%5B1%5D%29

y-%28-1%29=3%28x-2%29

Now, simplify and solve for y to put your new equation into the required slope-intercept form:
y-%28-1%29=3%28x-2%29
y%2B1=3x-6
y=3x-6-1
y=3x-7

Below, the red line is the given line, and the green line is the required line.