Question

Select the equation of a line that is perpendicular to the line on the graph and passes through the point (-1, 2).

Answer 1

Perpendicular lines of a slope that, if multiplied with the slope of a line, equals -1.

That is:

(slope of line) * (slope of perpendicular line) = -1

So, if you know the slope of the line you start with, you can find the slope of the perpendicular line with this.

Then you can use the point-slope form of a line to find the final equation.

Answer 2

So, I have to get the X put of my options, and whichever equals -1 is my answer?

Answer 3

First, find the slope of the line in the graph.

Answer 4

(-2, 0) (0, -1)
\[Y = mx+b\]
Don't I put my X values in?

Answer 5

\[slope = \frac{y_2 - y_1}{x_2 - x_1}\]

Answer 6

Ohhh ,whoops.

\[\frac{ ^{-}1 - 0 }{ 0 - ^{-}2 } = -\frac{ 1 }{ 2 }\]

Answer 7

There ya go. Now you can find the slope of the line that is perpendicular to that.

(slope of line)*(slope of perpendicular line) = -1

Answer 8

\[-\frac{ 1 }{ 2 } \div -1 = \] slope of perpendicular line?

Answer 9

\[\frac{ 1 }{ 2 }\]

Answer 10

let "a" be the slope of the line we know, and "m" be the slope of the perpendicular line:

\[a*m = -1\]
\[\frac{-1}{2} * m = -1\]
\[m = -1 * \frac{2}{-1} = 2\]

Answer 11

Okay, so \[Y = -\frac{ 1 }{ 2 }x + 2?\]

Answer 12

No. We just found the SLOPE of the perpendicular line.

Now we need to use the point-slope form of a line to find the final equation.

\[y - y_o = m(x - x_o)\]

Answer 13

What are the subscripts?

Answer 14

They just tell us that they are values for a point. Those are where you'll plug in your given x and y (the point that the line passes through)

Answer 15

Am I replacing \[y - y _{o}\] and \[x - x_o\] with my X and Y values?..

Answer 16

Like (-2, 0) and (0, -1)?

Answer 17

The point you are given for the line to go through is in the form:
\[(x_o , y_o) \]

You'll only replace the x and y that have the subscript, and then solve for the y that doesn't.

Answer 18

You are given the point (-1,2), and you have a slope of 2.

\[y - 2 = 2(x - (-1))\]

Solve for y, and you're done.

Answer 19

\[y = 2x + 4\]

Answer 20

right?

Answer 21

Correct :)

Answer 22

Thank you!!