Thread: line

Write an equation of the line that is parallel to the given line that passes through the given point.


y=-2x + 3 (y=4. x=4)?
Please Help

So y=mx+b. Since the new line must be parrallel to the first line, we know that the slope is the same (m=slope=-2). So y=-2x+b. Now we use the point we were given (4,4). So 4=-2(4)+b. Then we solve for b. So b=12.
So the new line that is parrallel is y=-2x+12.

another approach is to use the point-slope form.. in this case, there is no variable to solve.. just distribution and arithmetic..

$\displaystyle y - y_o = m(x - x_o)$, where m is the slope and $\displaystyle (x_o,y_o)$ is the given point..

$\displaystyle y - 4 = -2(x - 4) \implies y = -2x + 8 + 4 = -2x + 12 $