SOLUTION: FIND AN EQUATION OF THE LINE CONTAINING THE POINT (-4,3) AND PARALLEL TO THE LINE 5x-3y=12.

Algebra ->  Equations -> SOLUTION: FIND AN EQUATION OF THE LINE CONTAINING THE POINT (-4,3) AND PARALLEL TO THE LINE 5x-3y=12.      Log On


   

Question 127414: FIND AN EQUATION OF THE LINE CONTAINING THE POINT (-4,3) AND PARALLEL TO THE LINE 5x-3y=12.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!



First convert the standard equation 5x-3y=12 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-3y=12 Start with the given equation


5x-3y-5x=12-5x Subtract 5x from both sides


-3y=-5x%2B12 Simplify


%28-3y%29%2F%28-3%29=%28-5x%2B12%29%2F%28-3%29 Divide both sides by -3 to isolate y


y+=+%28-5x%29%2F%28-3%29%2B%2812%29%2F%28-3%29 Break up the fraction on the right hand side


y+=+%285%2F3%29x-4 Reduce and simplify


The original equation 5x-3y=12 (standard form) is equivalent to y+=+%285%2F3%29x-4 (slope-intercept form)


The equation y+=+%285%2F3%29x-4 is in the form y=mx%2Bb where m=5%2F3 is the slope and b=-4 is the y intercept.








Now let's find the equation of the line that is parallel to y=%285%2F3%29x-4 which goes through (-4,3)

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=%285%2F3%29%2Ax-4 which is also 5%2F3). Also since the unknown line goes through (-4,3), 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-3=%285%2F3%29%2A%28x%2B4%29 Plug in m=5%2F3, x%5B1%5D=-4, and y%5B1%5D=3



y-3=%285%2F3%29%2Ax-%285%2F3%29%28-4%29 Distribute 5%2F3



y-3=%285%2F3%29%2Ax%2B20%2F3 Multiply



y=%285%2F3%29%2Ax%2B20%2F3%2B3Add 3 to both sides to isolate y

y=%285%2F3%29%2Ax%2B20%2F3%2B9%2F3 Make into equivalent fractions with equal denominators



y=%285%2F3%29%2Ax%2B29%2F3 Combine the fractions



y=%285%2F3%29%2Ax%2B29%2F3 Reduce any fractions

So the equation of the line that is parallel to y=%285%2F3%29%2Ax-4 and goes through (-4,3) is y=%285%2F3%29%2Ax%2B29%2F3


So here are the graphs of the equations y=%285%2F3%29%2Ax-4 and y=%285%2F3%29%2Ax%2B29%2F3



graph of the given equation y=%285%2F3%29%2Ax-4 (red) and graph of the line y=%285%2F3%29%2Ax%2B29%2F3(green) that is parallel to the given graph and goes through (-4,3)