SOLUTION: Determine whether the graphs of each pair of equations are parallel,perpendicular, or neither. 23) 7x+3y=4 3x-7y=1

Algebra ->  Linear-equations -> SOLUTION: Determine whether the graphs of each pair of equations are parallel,perpendicular, or neither. 23) 7x+3y=4 3x-7y=1      Log On


   

Question 175268This question is from textbook Glencoe Algebra Concepts and Applications
: Determine whether the graphs of each pair of equations are parallel,perpendicular, or neither. 23) 7x+3y=4
3x-7y=1 This question is from textbook Glencoe Algebra Concepts and Applications

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

7x%2B3y=4 Start with the first equation.


3y=4-7x Subtract 7x from both sides.


3y=-7x%2B4 Rearrange the terms.


y=%28-7x%2B4%29%2F%283%29 Divide both sides by 3 to isolate y.


y=%28%28-7%29%2F%283%29%29x%2B%284%29%2F%283%29 Break up the fraction.


y=-%287%2F3%29x%2B4%2F3 Reduce.


So we can see that the equation y=-%287%2F3%29x%2B4%2F3 has a slope m=-7%2F3 and a y-intercept b=4%2F3.


3x-7y=1 Now move onto the second equation.


-7y=1-3x Subtract 3x from both sides.


-7y=-3x%2B1 Rearrange the terms.


y=%28-3x%2B1%29%2F%28-7%29 Divide both sides by -7 to isolate y.


y=%28%28-3%29%2F%28-7%29%29x%2B%281%29%2F%28-7%29 Break up the fraction.


y=%283%2F7%29x-1%2F7 Reduce.


So we can see that the equation y=%283%2F7%29x-1%2F7 has a slope m=3%2F7 and a y-intercept b=-1%2F7.


So the slope of the first line is m=-7%2F3 and the slope of the second line is m=3%2F7.


Notice how the slope of the second line m=3%2F7 is simply the negative reciprocal of the slope of the first line m=-7%2F3.


In other words, if you flip the fraction of the second slope and change its sign, you'll get the first slope. So this means that y=-%287%2F3%29x%2B4%2F3 and y=%283%2F7%29x-1%2F7 are perpendicular lines.