Question

Which of the following lines is perpendicular to the line 2x - y = 4?

Answer 1

First let's make the given equation equal to y. To do this subtract 2x to both sides

2x - 2x - y = 4 - 2x

0 - y = 4 - 2x

-y = 4 - 2x

Now to completely isolate y you must get rid of the negative. To do this divide the negative to both sides

-y/- = (4 - 2x)/-

y = 2x - 4

^^^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

In this case the slope of the line given is 2

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.

For the lines to be perpendicular the other line must have a slope of $\frac{-1}{2}$

You didn't give any options, but the answer will be the line with the slope of $\frac{-1}{2}$. The formatting should look similar to this

y = $\frac{-1}{2}$x + b

KEEP IN MIND: The b can have any value instead. The b depends on the y-intercept of the line

 

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer 2

Two lines are perpendicular if in its intersection there are four angles of 90° formed.

We will find that a perpendicular line to 2x - y = 4 is: y = (-1/2)*x + c

Where c can be any real value.

A general line in slope-intercept form is:

y = a*x +b

Where a is the slope and b is the y-intercept.

A perpendicular line to this one must have a slope equal to the opposite of the inverse of the slope of this one.

Thus the slope of the perpendicular line should be:

a' = -(1/a).

And the y-intercept of the perpendicular line has no restrictions, so it can be anything you want.

Now what we need to do is to rewrite our initial line in the slope-intercept form.

2x - y = 4

-2x + y = -4

y = 2x - 4

Now we know that the slope of this line is a = 2

Then the slope of the perpendicular one will be:

a'  = -(1/a) = -1/2

Then the general form of a perpendicular line to ours is:

y = (-1/2)*x + c

Where c can be any real value.

If you want to learn more, you can read:

https://brainly.com/question/11064712