SOLUTION: Given the line with equation y = 4/3x � 7, find an equation for the line that contains the point (6, 4) and is parallel to the givven line. I am a retired music teacher. I have

Question 264495: Given the line with equation y = 4/3x � 7, find an equation for the line that contains the point (6, 4) and is parallel to the givven line.
I am a retired music teacher. I have several music students that I have been teaching for several years at no cost to the student. I have a student that needs help and I know some algebra. However, I'm pretty much lost in algebra 2.

Bob Rietzke
bob@rietzke.net

Answer by jim_thompson5910(35256) (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 (its from the slope of which is also ). Also since the unknown line goes through (6,4), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

where m is the slope and (,) is the given point

Plug in , , and

Distribute

Multiply

Add to both sides to isolate y

Make into equivalent fractions with equal denominators

Combine the fractions

Reduce any fractions

So the equation of the line that is parallel to and goes through (,) is

So here are the graphs of the equations and

graph of the given equation (red) and graph of the line (green) that is parallel to the given graph and goes through (,)

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