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

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

Start with the first equation.

So we can see that the equation has a slope and a y-intercept .

Now move onto the second equation.

So we can see that the equation has a slope and a y-intercept .

So the slope of the first line is and the slope of the second line is .

Notice how the slope of the first line is simply the negative reciprocal of the slope of the second line .

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 and are perpendicular lines.

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

Graph of and
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