Question

Help! Is it parallel, perpendicular, or neither? Thanks *ignore handwriting*

Answer 1

First let's make both equations equal to y. One of them already is ( y = x) so let's make x + y = -2 equal to y . To do this subtract x to both sides

x - x + y = -2 - x

0 + y = -2 - x

y = -x - 2

Now we can compare the two equations properly

y = x

y = -x - 2

Remember that the slope intercept formula (which both of these equations are in) is:

y = mx + b

m is the slope

b is the y-intercept

For the equation y = x

slope = 1

y - intercept = (0, 0)

For equation y = -x - 2

slope = -1

y - intercept = (0, -2)

For lines to be parallel the slope must be the same

For lines to be perpendicular the slopes must be opposite reciprocals of each other. What this means is that they must have slopes that have numerator and denominators switch the places AND have the opposite signs of each other.

In this case the lines are perpendicular. The slope of y = x is 1 (or $\frac{1}{1}$) the opposite reciprocal of 1 is -1 (or $\frac{-1}{1}$). Since this is the slope of the line x + y = -2 these lines are perpendicular!

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer 2

These lines are perpendicular!
y = x
y = -x–2
The slopes are reciprocals of each other, so they are perpendicular.