ShmoopTube

00:02

Here’s your shmoop du jour, brought to you by translated lines.

00:06

Sometimes they're even foggier than Blurred Lines.

00:10

The line y = -2x + 4 is reflected over the y-axis, then translated down one unit and right two units.

00:18

What is its new y-intercept?

00:23

All right, so we’re talking about a line… on a graph…

00:25

The line in question is y = -2x + 4.

00:28

Here’s our graph. Now…where would that line go?

00:32

Well, if y is zero, then x would have to be 2… so let’s draw a point on the x axis at (2,0).

00:39

If we want x to be zero…it would create a point of intersection at the y-axis at (0,4).

00:44

So…la la la… connecting the dots…

00:46

And…there’s our line.

00:48

Now…what does this problem want us to do with it?

00:51

Cast it into a lake and see if we can catch ourselves a trout?

00:54

Uh, no. Wrong kinda line. First it wants us to REFLECT the line across the y-axis.

01:00

Well, one point is right ON the y-axis, so… that guy ain’t goin’ nowhere.

01:04

In fact, the entire line is pretty much just going to pivot around that point, sorta like a hinge.

01:10

What about our other point, the one at (2,0)?

01:13

Yeah, that one gets reflected across, and becomes (-2,0).

01:16

So our new line looks like this: Last step… we need to translate… or shift…

01:21

the line down one unit, and two to the right.

01:24

This time we move both points…like so…

01:27

…and there’s our line’s final resting place.

01:29

So…where’s the new y-intercept?

01:31

Right here… at negative 1. And we have our answer.

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