steps in paralled equation y=-1/3x-4; through (-6,-3)

Question

The steps using the words Origin, Ordered pair, x- or y- intercept, slope and reciprocal

Answer 1

Any parallel line to a given line must have the same slope but a different intercept.

 

Thus the equation for this new parallel line must be y = -x/3 + c, where c represents an intercept we have to find.

 

We can find this intercept by knowing the line passes through the point (-6,-3). If x = -6, then y = -(-6)/3 + c

 

Then y = 2 + c. However, in the ordered pair (-6,-3), y=-3. Therefore, c must be -5.

 

We plug this in to our equation for the new line to obtain f(x) = y = -x/3 - 5

 

We can check that equation is correct by noting that f(-6) = -3