SOLUTION: could someone please help. The equation of the line that goes through the point ( 7 ,2 ) and is parallel to the line 5 x + 3 y = 5 can be written in the form y = mx+b where m is

Algebra ->  Functions -> SOLUTION: could someone please help. The equation of the line that goes through the point ( 7 ,2 ) and is parallel to the line 5 x + 3 y = 5 can be written in the form y = mx+b where m is      Log On


   

Question 184084: could someone please help.
The equation of the line that goes through the point ( 7 ,2 ) and is parallel to the line 5 x + 3 y = 5 can be written in the form y = mx+b where m is:
and where b is:

Found 2 solutions by vleith, jim_thompson5910:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Get the original equation in the form y+=+mx+%2B++b
5+x+%2B+3+y+=+5
3y+=+-5x+%2B+5
y+=+-%285%2F3%29x+%2B+5%2F3
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 -%285%2F3%29 (its from the slope of y=%28-%285%2F3%29%29%2Ax%2B%285%2F3%29 which is also -%285%2F3%29). Also since the unknown line goes through (7,2), 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-2=%28-%285%2F3%29%29%2A%28x-7%29 Plug in m=-%285%2F3%29, x%5B1%5D=7, and y%5B1%5D=2



y-2=%28-%285%2F3%29%29%2Ax%2B%28%285%2F3%29%29%287%29 Distribute -%285%2F3%29



y-2=%28-%285%2F3%29%29%2Ax-0%2F3 Multiply



y=%28-%285%2F3%29%29%2Ax-0%2F3%2B2Add 2 to both sides to isolate y

y=%28-%285%2F3%29%29%2Ax-0%2F3%2B6%2F3 Make into equivalent fractions with equal denominators



y=%28-%285%2F3%29%29%2Ax%2B6%2F3 Combine the fractions



y=%28-%285%2F3%29%29%2Ax%2B2 Reduce any fractions

So the equation of the line that is parallel to y=%28-%285%2F3%29%29%2Ax%2B%285%2F3%29 and goes through (7,2) is y=%28-%285%2F3%29%29%2Ax%2B2


So here are the graphs of the equations y=%28-%285%2F3%29%29%2Ax%2B%285%2F3%29 and y=%28-%285%2F3%29%29%2Ax%2B2



graph of the given equation y=%28-%285%2F3%29%29%2Ax%2B%285%2F3%29 (red) and graph of the line y=%28-%285%2F3%29%29%2Ax%2B2(green) that is parallel to the given graph and goes through (7,2)

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%2F3 (its from the slope of y=%28-5%2F3%29%2Ax%2B5%2F3 which is also -5%2F3). Also since the unknown line goes through (7,2), 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-2=%28-5%2F3%29%2A%28x-7%29 Plug in m=-5%2F3, x%5B1%5D=7, and y%5B1%5D=2



y-2=%28-5%2F3%29%2Ax%2B%285%2F3%29%287%29 Distribute -5%2F3



y-2=%28-5%2F3%29%2Ax%2B35%2F3 Multiply



y=%28-5%2F3%29%2Ax%2B35%2F3%2B2Add 2 to both sides to isolate y

y=%28-5%2F3%29%2Ax%2B35%2F3%2B6%2F3 Make into equivalent fractions with equal denominators



y=%28-5%2F3%29%2Ax%2B41%2F3 Combine the fractions



y=%28-5%2F3%29%2Ax%2B41%2F3 Reduce any fractions

So the equation of the line that is parallel to y=%28-5%2F3%29%2Ax%2B5%2F3 and goes through (7,2) is y=%28-5%2F3%29%2Ax%2B41%2F3


So here are the graphs of the equations y=%28-5%2F3%29%2Ax%2B5%2F3 and y=%28-5%2F3%29%2Ax%2B41%2F3



graph of the given equation y=%28-5%2F3%29%2Ax%2B5%2F3 (red) and graph of the line y=%28-5%2F3%29%2Ax%2B41%2F3(green) that is parallel to the given graph and goes through (7,2)