SOLUTION: Sketch a second line parallel to the given line. The second line should cross the y-axis as specified. Parallel to y=-3x, passing through (0,4). Thanks!

Algebra ->  Linear-equations -> SOLUTION: Sketch a second line parallel to the given line. The second line should cross the y-axis as specified. Parallel to y=-3x, passing through (0,4). Thanks!      Log On


   

Question 711980: Sketch a second line parallel to the given line. The second line should cross the y-axis as specified.
Parallel to y=-3x, passing through (0,4).
Thanks!
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Since any two parallel lines have the same slope we know the slope of the unknown line is -3 (its from the slope of y=-3%2Ax%2B0 which is also -3). Also since the unknown line goes through (0,4), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y-4=-3%2A%28x-0%29 Plug in m=-3, x%5B1%5D=0, and y%5B1%5D=4



y-4=-3%2Ax%2B%283%29%280%29 Distribute -3



y-4=-3%2Ax-0 Multiply



y=-3%2Ax-0%2B4Add 4 to both sides to isolate y

y=-3%2Ax%2B4 Combine like terms

So the equation of the line that is parallel to y=-3%2Ax%2B0 and goes through (0,4) is y=-3%2Ax%2B4


So here are the graphs of the equations y=-3%2Ax%2B0 and y=-3%2Ax%2B4



graph of the given equation y=-3%2Ax%2B0 (red) and graph of the line y=-3%2Ax%2B4(green) that is parallel to the given graph and goes through (0,4)