SOLUTION: Write the equation of the L satisfying the given geometric conditions. L passes through point (-4,3) and is parallel to the line equation y=2x+1

Algebra ->  Linear-equations -> SOLUTION: Write the equation of the L satisfying the given geometric conditions. L passes through point (-4,3) and is parallel to the line equation y=2x+1      Log On


   

Question 117783: Write the equation of the L satisfying the given geometric conditions.
L passes through point (-4,3) and is parallel to the line equation y=2x+1
Found 2 solutions by jim_thompson5910, Fombitz:
Answer by jim_thompson5910(35256) 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 2 (its from the slope of y=2%2Ax%2B1 which is also 2). Also since the unknown line goes through (-4,3), 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-3=2%2A%28x%2B4%29 Plug in m=2, x%5B1%5D=-4, and y%5B1%5D=3



y-3=2%2Ax-%282%29%28-4%29 Distribute 2



y-3=2%2Ax%2B8 Multiply



y=2%2Ax%2B8%2B3Add 3 to both sides to isolate y

y=2%2Ax%2B11 Combine like terms

So the equation of the line that is parallel to y=2%2Ax%2B1 and goes through (-4,3) is y=2%2Ax%2B11


So here are the graphs of the equations y=2%2Ax%2B1 and y=2%2Ax%2B11



graph of the given equation y=2%2Ax%2B1 (red) and graph of the line y=2%2Ax%2B11(green) that is parallel to the given graph and goes through (-4,3)

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Here is the graph of your original line, y=2x+1, and the point of interest.

Parallel lines have the same slope.
Use the point slope form of a line.
y-y%5B1%5D=m%28x-x%5B1%5D%29
y-3=2%28x-%28-4%29%29
y-3=2%28x%2B4%29
y-3=2x%2B8
y=2x%2B11