SOLUTION: Determine whether the lines are parallel, perpendicular, or neither y = -1/4x + 8 y = 4x + 10

Algebra ->  Graphs -> SOLUTION: Determine whether the lines are parallel, perpendicular, or neither y = -1/4x + 8 y = 4x + 10      Log On


   

Question 151476: Determine whether the lines are parallel, perpendicular, or neither
y = -1/4x + 8
y = 4x + 10
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

y=-%281%2F4%29x%2B8 Start with the first equation.


So we can see that the equation y=-%281%2F4%29x%2B8 has a slope m=-1%2F4 and a y-intercept b=8.


y=4x%2B10 Now move onto the second equation.


So we can see that the equation y=4%2Ax%2B10 has a slope m=4 and a y-intercept b=10.


So the slope of the first line is m=-1%2F4 and the slope of the second line is m=4.


Notice how the slope of the first line m=-1%2F4 is simply the negative reciprocal of the slope of the second line m=4.


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=-%281%2F4%29x%2B8 and y=4%2Ax%2B10 are perpendicular lines.


As further confirmation, you can graph the two lines and you'll see that they are perpendicular

Graph of y=-%281%2F4%29x%2B8 and y=4%2Ax%2B10