SOLUTION: 32. Write an equation of the line containing the given point and parallel to the given line. Express in form y = mx + b (-5,6); 6x=5y+3

Algebra ->  Coordinate-system -> SOLUTION: 32. Write an equation of the line containing the given point and parallel to the given line. Express in form y = mx + b (-5,6); 6x=5y+3      Log On


   

Question 237338: 32. Write an equation of the line containing the given point and parallel to the given line. Express in form y = mx + b
(-5,6); 6x=5y+3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
6x=5y%2B3 Start with the given equation.


6x-3=5y Subtract 3 from both sides.


5y=6x-3 Rearrange the equation.


y=%286%2F5%29x-3%2F5 Divide every term by 5 to isolate 'y'.


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 6%2F5 (its from the slope of y=%286%2F5%29%2Ax-3%2F5 which is also 6%2F5). Also since the unknown line goes through (-5,6), 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-6=%286%2F5%29%2A%28x%2B5%29 Plug in m=6%2F5, x%5B1%5D=-5, and y%5B1%5D=6



y-6=%286%2F5%29%2Ax-%286%2F5%29%28-5%29 Distribute 6%2F5



y-6=%286%2F5%29%2Ax%2B30%2F5 Multiply



y=%286%2F5%29%2Ax%2B30%2F5%2B6Add 6 to both sides to isolate y

y=%286%2F5%29%2Ax%2B30%2F5%2B30%2F5 Make into equivalent fractions with equal denominators



y=%286%2F5%29%2Ax%2B60%2F5 Combine the fractions



y=%286%2F5%29%2Ax%2B12 Reduce any fractions

So the equation of the line that is parallel to y=%286%2F5%29%2Ax-3%2F5 and goes through (-5,6) is y=%286%2F5%29%2Ax%2B12


So here are the graphs of the equations y=%286%2F5%29%2Ax-3%2F5 and y=%286%2F5%29%2Ax%2B12



graph of the given equation y=%286%2F5%29%2Ax-3%2F5 (red) and graph of the line y=%286%2F5%29%2Ax%2B12(green) that is parallel to the given graph and goes through (-5,6)