SOLUTION: The equation of the line that goes through the point ( 6 ,2 ) and is parallel to the line 2 x + 5 y = 4 can be written in the form y = mx+b where m is:_ and where b is:_

Algebra ->  Length-and-distance -> SOLUTION: The equation of the line that goes through the point ( 6 ,2 ) and is parallel to the line 2 x + 5 y = 4 can be written in the form y = mx+b where m is:_ and where b is:_       Log On


   

Question 274923: The equation of the line that goes through the point ( 6 ,2 ) and is parallel to the line 2 x + 5 y = 4 can be written in the form y = mx+b where m is:_
and where b is:_
Found 2 solutions by JBarnum, jim_thompson5910:
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
just put the equation in the y-intercept form u have shown
2x%2B5y=4
5y=4-2x
y=%284%2F5%29%2B%28-2%2F5%29x
y=%28-2%2F5%29x%2B%284%2F5%29
y=mx%2Bb
highlight%28m=-2%2F5%29
to find b you will need to put the point in the eqaution and solve for b
2=%28-2%2F5%29%286%29%2Bb
2=%28-12%2F5%29%2Bb
%2810%2F5%29%2B%2812%2F5%29=b
highlight%2822%2F5=b%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First solve for y to get y=-%285%2F2%29x%2B4%2F5

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=%28-5%2F2%29%2Ax%2B4%2F5 which is also -5%2F2). Also since the unknown line goes through (6,2), 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%2F2%29%2A%28x-6%29 Plug in m=-5%2F2, x%5B1%5D=6, and y%5B1%5D=2



y-2=%28-5%2F2%29%2Ax%2B%285%2F2%29%286%29 Distribute -5%2F2



y-2=%28-5%2F2%29%2Ax%2B30%2F2 Multiply



y=%28-5%2F2%29%2Ax%2B30%2F2%2B2Add 2 to both sides to isolate y

y=%28-5%2F2%29%2Ax%2B30%2F2%2B4%2F2 Make into equivalent fractions with equal denominators



y=%28-5%2F2%29%2Ax%2B34%2F2 Combine the fractions



y=%28-5%2F2%29%2Ax%2B17 Reduce any fractions

So the equation of the line that is parallel to y=%28-5%2F2%29%2Ax%2B4%2F5 and goes through (6,2) is y=%28-5%2F2%29%2Ax%2B17


So here are the graphs of the equations y=%28-5%2F2%29%2Ax%2B4%2F5 and y=%28-5%2F2%29%2Ax%2B17



graph of the given equation y=%28-5%2F2%29%2Ax%2B4%2F5 (red) and graph of the line y=%28-5%2F2%29%2Ax%2B17(green) that is parallel to the given graph and goes through (6,2)