SOLUTION: Find the equation of the lines if: The line is parallel to the line 3x-7y=15 and has an x-intercept of -5.

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Question 87577: Find the equation of the lines if:
The line is parallel to the line 3x-7y=15 and has an x-intercept of -5.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First convert 3x-7y=15 into slope-intercept form

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)


3x-7y=15 Start with the given equation


3x-7y-3x=15-3x Subtract 3x from both sides


-7y=-3x%2B15 Simplify


%28-7y%29%2F%28-7%29=%28-3x%2B15%29%2F%28-7%29 Divide both sides by -7 to isolate y


y+=+%28-3x%29%2F%28-7%29%2B%2815%29%2F%28-7%29 Break up the fraction on the right hand side


y+=+%283%2F7%29x-15%2F7 Reduce and simplify


The original equation 3x-7y=15 (standard form) is equivalent to y+=+%283%2F7%29x-15%2F7 (slope-intercept form)


The equation y+=+%283%2F7%29x-15%2F7 is in the form y=mx%2Bb where m=3%2F7 is the slope and b=-15%2F7 is the y intercept.





Since the line has an x-intercept of -5, this means the line goes through the point (-5,0)


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 3%2F7 (its from the slope of y=%283%2F7%29%2Ax-15%2F7 which is also 3%2F7). Also since the unknown line goes through (-5,0), 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=%283%2F7%29%2A%28x%2B5%29 Plug in m=3%2F7, x%5B1%5D=-5, and y%5B1%5D=0



y-0=%283%2F7%29%2Ax-%283%2F7%29%28-5%29 Distribute 3%2F7



y-0=%283%2F7%29%2Ax%2B15%2F7 Multiply



y=%283%2F7%29%2Ax%2B15%2F7%2B0Add 0 to both sides to isolate y

y=%283%2F7%29%2Ax%2B15%2F7%2B0%2F7 Make into equivalent fractions with equal denominators



y=%283%2F7%29%2Ax%2B15%2F7 Combine the fractions



y=%283%2F7%29%2Ax%2B15%2F7 Reduce any fractions

So the equation of the line that is parallel to y=%283%2F7%29%2Ax-15%2F7 and goes through (-5,0) is y=%283%2F7%29%2Ax%2B15%2F7


So here are the graphs of the equations y=%283%2F7%29%2Ax-15%2F7 and y=%283%2F7%29%2Ax%2B15%2F7



graph of the given equation y=%283%2F7%29%2Ax-15%2F7 (red) and graph of the line y=%283%2F7%29%2Ax%2B15%2F7(green) that is parallel to the given graph and goes through (-5,0)