SOLUTION: Find the equation of the line parallel to 5x-2y=10 that goes through (4,10) in slope intercept form.

Algebra ->  Graphs -> SOLUTION: Find the equation of the line parallel to 5x-2y=10 that goes through (4,10) in slope intercept form.      Log On


   

Question 955028: Find the equation of the line parallel to 5x-2y=10 that goes through (4,10) in slope intercept form.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the line parallel to 5x-2y=10=> 5x-10=2y=> %285%2F2%29x-5=y
that goes through (4,10)
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-5 which is also 5%2F2). Also since the unknown line goes through (4,10), 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-10=%285%2F2%29%2A%28x-4%29 Plug in m=5%2F2, x%5B1%5D=4, and y%5B1%5D=10



y-10=%285%2F2%29%2Ax-%285%2F2%29%284%29 Distribute 5%2F2



y-10=%285%2F2%29%2Ax-20%2F2 Multiply



y=%285%2F2%29%2Ax-20%2F2%2B10Add 10 to both sides to isolate y

y=%285%2F2%29%2Ax-20%2F2%2B20%2F2 Make into equivalent fractions with equal denominators



y=%285%2F2%29%2Ax%2B0%2F2 Combine the fractions



y=%285%2F2%29%2Ax%2B0 Reduce any fractions

So the equation of the line that is parallel to y=%285%2F2%29%2Ax-5 and goes through (4,10) is y=%285%2F2%29%2Ax%2B0


So here are the graphs of the equations y=%285%2F2%29%2Ax-5 and y=%285%2F2%29%2Ax%2B0



graph of the given equation y=%285%2F2%29%2Ax-5 (red) and graph of the line y=%285%2F2%29%2Ax%2B0(green) that is parallel to the given graph and goes through (4,10)