SOLUTION: whats the equation in the form of Y=mx+b through(3,-5) parallel to y=4x+3

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: whats the equation in the form of Y=mx+b through(3,-5) parallel to y=4x+3       Log On


   

Question 459364: whats the equation in the form of Y=mx+b through(3,-5) parallel to y=4x+3
Answer by MathLover1(20850) 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 4 (its from the slope of y=4%2Ax%2B3 which is also 4). Also since the unknown line goes through (3,-5), 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%2B5=4%2A%28x-3%29 Plug in m=4, x%5B1%5D=3, and y%5B1%5D=-5



y%2B5=4%2Ax-%284%29%283%29 Distribute 4



y%2B5=4%2Ax-12 Multiply



y=4%2Ax-12-5Subtract -5 from both sides to isolate y

y=4%2Ax-17 Combine like terms

So the equation of the line that is parallel to y=4%2Ax%2B3 and goes through (3,-5) is y=4%2Ax-17


So here are the graphs of the equations y=4%2Ax%2B3 and y=4%2Ax-17



graph of the given equation y=4%2Ax%2B3 (red) and graph of the line y=4%2Ax-17(green) that is parallel to the given graph and goes through (3,-5)