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

Algebra ->  Graphs -> 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       Log On


   

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) 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%2F3 (its from the slope of y=%284%2F3%29%2Ax-7 which is also 4%2F3). 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:

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=%284%2F3%29%2A%28x-6%29 Plug in m=4%2F3, x%5B1%5D=6, and y%5B1%5D=4



y-4=%284%2F3%29%2Ax-%284%2F3%29%286%29 Distribute 4%2F3



y-4=%284%2F3%29%2Ax-24%2F3 Multiply



y=%284%2F3%29%2Ax-24%2F3%2B4Add 4 to both sides to isolate y

y=%284%2F3%29%2Ax-24%2F3%2B12%2F3 Make into equivalent fractions with equal denominators



y=%284%2F3%29%2Ax-12%2F3 Combine the fractions



y=%284%2F3%29%2Ax-4 Reduce any fractions

So the equation of the line that is parallel to y=%284%2F3%29%2Ax-7 and goes through (6,4) is y=%284%2F3%29%2Ax-4


So here are the graphs of the equations y=%284%2F3%29%2Ax-7 and y=%284%2F3%29%2Ax-4



graph of the given equation y=%284%2F3%29%2Ax-7 (red) and graph of the line y=%284%2F3%29%2Ax-4(green) that is parallel to the given graph and goes through (6,4)