SOLUTION: Write the equation of each line. Give the answer in standard form using only integers as the coefficients. The line through (3,4) that is parallel to the line 5x+3y=9 The ans

Algebra ->  Linear-equations -> SOLUTION: Write the equation of each line. Give the answer in standard form using only integers as the coefficients. The line through (3,4) that is parallel to the line 5x+3y=9 The ans      Log On


   

Question 118013: Write the equation of each line. Give the answer in standard form using only integers as the coefficients.
The line through (3,4) that is parallel to the line 5x+3y=9
The answer is 5x+3y=27
How do I work the problem to get the above answer?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First convert 5x+3y=9 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)


5x%2B3y=9 Start with the given equation


5x%2B3y-5x=9-5x Subtract 5x from both sides


3y=-5x%2B9 Simplify


%283y%29%2F%283%29=%28-5x%2B9%29%2F%283%29 Divide both sides by 3 to isolate y


y+=+%28-5x%29%2F%283%29%2B%289%29%2F%283%29 Break up the fraction on the right hand side


y+=+%28-5%2F3%29x%2B3 Reduce and simplify


The original equation 5x%2B3y=9 (standard form) is equivalent to y+=+%28-5%2F3%29x%2B3 (slope-intercept form)


The equation y+=+%28-5%2F3%29x%2B3 is in the form y=mx%2Bb where m=-5%2F3 is the slope and b=3 is the y intercept.





Now let's find the equation of the line through (3,4) that is parallel to the line y=%28-5%2F3%29x%2B3

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%2B3 which is also -5%2F3). Also since the unknown line goes through (3,4), 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-4=%28-5%2F3%29%2A%28x-3%29 Plug in m=-5%2F3, x%5B1%5D=3, and y%5B1%5D=4



y-4=%28-5%2F3%29%2Ax%2B%285%2F3%29%283%29 Distribute -5%2F3



y-4=%28-5%2F3%29%2Ax%2B15%2F3 Multiply



y=%28-5%2F3%29%2Ax%2B15%2F3%2B4Add 4 to both sides to isolate y

y=%28-5%2F3%29%2Ax%2B15%2F3%2B12%2F3 Make into equivalent fractions with equal denominators



y=%28-5%2F3%29%2Ax%2B27%2F3 Combine the fractions



y=%28-5%2F3%29%2Ax%2B9 Reduce any fractions

So the equation of the line that is parallel to y=%28-5%2F3%29%2Ax%2B3 and goes through (3,4) is y=%28-5%2F3%29%2Ax%2B9


So here are the graphs of the equations y=%28-5%2F3%29%2Ax%2B3 and y=%28-5%2F3%29%2Ax%2B9



graph of the given equation y=%28-5%2F3%29%2Ax%2B3 (red) and graph of the line y=%28-5%2F3%29%2Ax%2B9(green) that is parallel to the given graph and goes through (3,4)






Now let's convert y=%28-5%2F3%29x%2B9 to standard form

Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)
Convert from slope-intercept form (y = mx+b) to standard form (Ax+By = C)


y+=+%28-5%2F3%29x%2B9 Start with the given equation


3%2Ay+=+3%2A%28%28-5%2F3%29x%2B9%29 Multiply both sides by the LCD 3


3y+=+-5x%2B27 Distribute and multiply


3y%2B5x+=+-5x%2B27%2B5x Add 5x to both sides


5x%2B3y+=+27 Simplify


The original equation y+=+%28-5%2F3%29x%2B9 (slope-intercept form) is equivalent to 5x%2B3y+=+27 (standard form where A > 0)


The equation 5x%2B3y+=+27 is in the form Ax%2BBy+=+C where A+=+5, B+=+3 and C+=+27






So the answer is 5x%2B3y=27