SOLUTION: Find the equation of the line passing through the point (-2,-7) and parallel to the line 5x+y=4

Algebra ->  Graphs -> SOLUTION: Find the equation of the line passing through the point (-2,-7) and parallel to the line 5x+y=4      Log On


   

Question 1010762: Find the equation of the line passing through the point (-2,-7) and parallel to the line 5x+y=4
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the equation of the line passing through the point (-2,-7) and parallel to the line 5x+y=4
------------
Find the slope of the line, m
-----------
Parallel lines have the same slope.
---
Use y-y1 = m*(x-x1) where (x1,y1) is (-2,-7)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the equation of the line passing through the point (-2,-7)
and parallel to the line 5x%2By=4=>y=-5x%2B4

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 -5 (its from the slope of y=-5%2Ax%2B4 which is also -5). Also since the unknown line goes through (-2,-7), 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%2B7=-5%2A%28x%2B2%29 Plug in m=-5, x%5B1%5D=-2, and y%5B1%5D=-7



y%2B7=-5%2Ax%2B%285%29%28-2%29 Distribute -5



y%2B7=-5%2Ax-10 Multiply



y=-5%2Ax-10-7Subtract -7 from both sides to isolate y

y=-5%2Ax-17 Combine like terms

So the equation of the line that is parallel to y=-5%2Ax%2B4 and goes through (-2,-7) is y=-5%2Ax-17


So here are the graphs of the equations y=-5%2Ax%2B4 and y=-5%2Ax-17



graph of the given equation y=-5%2Ax%2B4 (red) and graph of the line y=-5%2Ax-17(green) that is parallel to the given graph and goes through (-2,-7)