SOLUTION: write the equation of the line passing through (5,8) and the parallel to 8x-9y=10

Algebra ->  Linear-equations -> SOLUTION: write the equation of the line passing through (5,8) and the parallel to 8x-9y=10       Log On


   

Question 474227: write the equation of the line passing through (5,8) and the parallel to 8x-9y=10
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

the line passing through (5,8) and the parallel to 8x-9y=10
write 8x-9y=10 in slope-intercept form
%288%2F9%29x-10%2F9=y
%280.9%29x-1.11=y
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 .9 (its from the slope of y=.9%2Ax-1.11 which is also .9). Also since the unknown line goes through (5,8), 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-8=.9%2A%28x-5%29 Plug in m=.9, x%5B1%5D=5, and y%5B1%5D=8



y-8=.9%2Ax-%28.9%29%285%29 Distribute .9



y-8=.9%2Ax-4.5 Multiply



y=.9%2Ax-4.5%2B8Add 8 to both sides to isolate y

y=.9%2Ax%2B3.5 Combine like terms

So the equation of the line that is parallel to y=.9%2Ax-1.11 and goes through (5,8) is y=.9%2Ax%2B3.5


So here are the graphs of the equations y=.9%2Ax-1.11 and y=.9%2Ax%2B3.5



graph of the given equation y=.9%2Ax-1.11 (red) and graph of the line y=.9%2Ax%2B3.5(green) that is parallel to the given graph and goes through (5,8)