SOLUTION: Determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither. 12x + 4y = 16 5y - 22 = -15x

Algebra ->  Graphs -> SOLUTION: Determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither. 12x + 4y = 16 5y - 22 = -15x      Log On


   

Question 166498: Determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither.
12x + 4y = 16
5y - 22 = -15x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First let's solve for "y" of the first equation 12x%2B4y=16


12x%2B4y=16 Start with the first equation.


4y=16-12x Subtract 12x from both sides.


4y=-12x%2B16 Rearrange the terms.


y=%28-12x%2B16%29%2F%284%29 Divide both sides by 4 to isolate y.


y=%28%28-12%29%2F%284%29%29x%2B%2816%29%2F%284%29 Break up the fraction.


y=-3x%2B4 Reduce.


So the equation y=-3x%2B4 is now in slope intercept form y=mx%2Bb where the slope is m=-3 and the y-intercept is b=4 note: the y-intercept is the point




Now let's solve for "y" of the second equation 5y-22=-15x


5y-22=-15x Start with the second equation.


5y=-15x%2B22 Add 22 to both sides.


y=%28-15x%2B22%29%2F%285%29 Divide both sides by 5 to isolate y.


y=%28-15x%29%2F%285%29%2B%2822%29%2F%285%29 Break up the fraction


y=-3x%2B22%2F5 Reduce



So the equation y=-3x%2B22%2F5 is now in slope intercept form y=mx%2Bb where the slope is m=-3 and the y-intercept is b=22%2F5 note: the y-intercept is the point



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So the slope of the first equation 12x%2B4y=16 is m=-3 and the slope of the second equation 5y-22=-15x is m=-3


Since the two slopes are equal, this means that the two lines are parallel.