SOLUTION: write the equation of a line through (-p, q) that is parallel to the line 3x-4y= 5

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Question 112963: write the equation of a line through (-p, q) that is parallel to the line 3x-4y= 5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First find the slope of 3x-4y= 5

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-4y=5 Start with the given equation


3x-4y-3x=5-3x Subtract 3x from both sides


-4y=-3x%2B5 Simplify


%28-4y%29%2F%28-4%29=%28-3x%2B5%29%2F%28-4%29 Divide both sides by -4 to isolate y


y+=+%28-3x%29%2F%28-4%29%2B%285%29%2F%28-4%29 Break up the fraction on the right hand side


y+=+%283%2F4%29x-5%2F4 Reduce and simplify


The original equation 3x-4y=5 (standard form) is equivalent to y+=+%283%2F4%29x-5%2F4 (slope-intercept form)


The equation y+=+%283%2F4%29x-5%2F4 is in the form y=mx%2Bb where m=3%2F4 is the slope and b=-5%2F4 is the y intercept.





So the slope of 3x-4y= 5 is 3%2F4


If you want to find the equation of line with a given a slope of 3%2F4 which goes through the point (-p, q), you can simply use the point-slope formula to find the equation:


---Point-Slope Formula---
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is the given point

So lets use the Point-Slope Formula to find the equation of the line

y-q=%283%2F4%29%28x-%28-p%29%29 Plug in m=3%2F4, x%5B1%5D=-p, and y%5B1%5D=q (these values are given)


y-q=%283%2F4%29x-%283%2F4%29%28-p%29 Distribute 3%2F4

y-q=%283%2F4%29x%2B%283%2F4%29p Multiply -3%2F4 and -p to get %283%2F4%29p

y=%283%2F4%29x%2B%283%2F4%29p%2Bq Add q to both sides to isolate y


So the equation parallel to 3x-4y= 5 and goes through (-p, q) is y=%283%2F4%29x%2B%283%2F4%29p%2Bq