QuestionFind the line equation through $(3,-1)$ parallel to $y=-2x-7$ . Show your steps.

Studdy Solution

STEP 1

Assumptions1. The line passes through the point $(3,-1)$ . The line is parallel to the line $y=-x-7$
3. The slope of a line parallel to another line is the same as the slope of the original line

STEP 2

First, we need to find the slope of the line that we are given. The equation of the line is in the form $y = mx + b$ , where $m$ is the slope. So, the slope of the line $y=-2x-7$ is $-2$ .
$m = -2$

STEP 3

Since the line we are trying to find is parallel to the line $y=-2x-7$ , it will have the same slope. So, the slope of the line we are trying to find is also $-2$ .
$m' = -2$

STEP 4

Now, we need to find the y-intercept of the line we are trying to find. We can use the point-slope form of the line, which is $y - y1 = m'(x - x1)$ , where $(x1, y1)$ is a point on the line.

STEP 5

Plug in the values for the slope $m'$ and the point $(x1, y1)$ into the point-slope form of the line.
$y - (-1) = -2(x -3)$

STEP 6

implify the equation to find the y-intercept.
$y +1 = -2x +6$

STEP 7

Rearrange the equation to the slope-intercept form, $y = mx + b$ .
$y = -2x +6 -1$

STEP 8

implify the equation.
$y = -2x +5$ The equation of the line that passes through the point $(3,-1)$ and is parallel to the line $y=-2x-7$ is $y = -2x +5$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms