SOLUTION: Write the equation of the line which passes through the point (2, 1) and is parallel to the line with equation y =5/2x+6.

Algebra ->  Equations -> SOLUTION: Write the equation of the line which passes through the point (2, 1) and is parallel to the line with equation y =5/2x+6.      Log On


   

Question 101150: Write the equation of the line which passes through the point (2, 1) and is parallel to the line with equation y =5/2x+6.
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 5%2F2 (its from the slope of y=%285%2F2%29%2Ax%2B6 which is also 5%2F2). Also since the unknown line goes through (2,1), 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-1=%285%2F2%29%2A%28x-2%29 Plug in m=5%2F2, x%5B1%5D=2, and y%5B1%5D=1



y-1=%285%2F2%29%2Ax-%285%2F2%29%282%29 Distribute 5%2F2



y-1=%285%2F2%29%2Ax-10%2F2 Multiply



y=%285%2F2%29%2Ax-10%2F2%2B1Add 1 to both sides to isolate y

y=%285%2F2%29%2Ax-10%2F2%2B2%2F2 Make into equivalent fractions with equal denominators



y=%285%2F2%29%2Ax-8%2F2 Combine the fractions



y=%285%2F2%29%2Ax-4 Reduce any fractions

So the equation of the line that is parallel to y=%285%2F2%29%2Ax%2B6 and goes through (2,1) is y=%285%2F2%29%2Ax-4


So here are the graphs of the equations y=%285%2F2%29%2Ax%2B6 and y=%285%2F2%29%2Ax-4



graph of the given equation y=%285%2F2%29%2Ax%2B6 (red) and graph of the line y=%285%2F2%29%2Ax-4(green) that is parallel to the given graph and goes through (2,1)