SOLUTION: Please assist me with this problem. Thanks! Write an equation of a line which is parallel to 5x + 2y = 4 and passes through the point (1,0).

Algebra ->  Inequalities -> SOLUTION: Please assist me with this problem. Thanks! Write an equation of a line which is parallel to 5x + 2y = 4 and passes through the point (1,0).      Log On


   

Question 90881: Please assist me with this problem. Thanks!
Write an equation of a line which is parallel to 5x + 2y = 4 and passes through the point (1,0).
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)
Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)


5x%2B2y=4 Start with the given equation


5x%2B2y-5x=4-5x Subtract 5x from both sides


2y=-5x%2B4 Simplify


%282y%29%2F%282%29=%28-5x%2B4%29%2F%282%29 Divide both sides by 2 to isolate y


y+=+%28-5x%29%2F%282%29%2B%284%29%2F%282%29 Break up the fraction on the right hand side


y+=+%28-5%2F2%29x%2B2 Reduce and simplify


The original equation 5x%2B2y=4 (standard form) is equivalent to y+=+%28-5%2F2%29x%2B2 (slope-intercept form)


The equation y+=+%28-5%2F2%29x%2B2 is in the form y=mx%2Bb where m=-5%2F2 is the slope and b=2 is the y intercept.





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%2B2 which is also -5%2F2). Also since the unknown line goes through (1,0), 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-0=%28-5%2F2%29%2A%28x-1%29 Plug in m=-5%2F2, x%5B1%5D=1, and y%5B1%5D=0



y-0=%28-5%2F2%29%2Ax%2B%285%2F2%29%281%29 Distribute -5%2F2



y-0=%28-5%2F2%29%2Ax%2B5%2F2 Multiply



y=%28-5%2F2%29%2Ax%2B5%2F2%2B0Add 0 to both sides to isolate y

y=%28-5%2F2%29%2Ax%2B5%2F2%2B0%2F2 Make into equivalent fractions with equal denominators



y=%28-5%2F2%29%2Ax%2B5%2F2 Combine the fractions



y=%28-5%2F2%29%2Ax%2B5%2F2 Reduce any fractions

So the equation of the line that is parallel to y=%28-5%2F2%29%2Ax%2B2 and goes through (1,0) is y=%28-5%2F2%29%2Ax%2B5%2F2


So here are the graphs of the equations y=%28-5%2F2%29%2Ax%2B2 and y=%28-5%2F2%29%2Ax%2B5%2F2



graph of the given equation y=%28-5%2F2%29%2Ax%2B2 (red) and graph of the line y=%28-5%2F2%29%2Ax%2B5%2F2(green) that is parallel to the given graph and goes through (1,0)

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Please assist me with this problem. Thanks!
Write an equation of a line which is parallel to 5x + 2y = 4 and passes through the point (1,0).
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The given line has slope m=-5/2
The line you want has form y=mx+b where m=-5/2,y=0 when x=1; solve for b:
0=(-5/2)1+b
b=(5/2)
EQUATION:
y = (-5/2)x + (5/2)
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Cheers,
Stan H.