QuestionFind the equation of line $\ell$ , perpendicular to $y=-10x-8$ and passing through $(2,2)$ .

Studdy Solution

STEP 1

Assumptions1. The equation of line $k$ is $y=-10x-8$ . Line $\ell$ is perpendicular to line $k$
3. Line $\ell$ passes through the point $(,)$

STEP 2

The slope of a line given by the equation $y=mx+b$ is $m$ . So, the slope of line $k$ is $-10$ .

STEP 3

The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. So, the slope of line $\ell$ , which is perpendicular to line $k$ , is the negative reciprocal of $-10$ .
$m_{\ell} = -\frac{1}{m_k}$

STEP 4

Plug in the value for the slope of line $k$ to find the slope of line $\ell$ .
$m_{\ell} = -\frac{1}{-10}$

STEP 5

Calculate the slope of line $\ell$ .
$m_{\ell} = -\frac{1}{-10} =0.1$

STEP 6

The equation of a line can be written in the form $y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept. We know the slope of line $\ell$ and a point $(x1, y1)$ on the line, so we can use the point-slope form of a line to find the equation of line $\ell$ .
$y - y1 = m(x - x1)$

STEP 7

Plug in the values for the slope of line $\ell$ and the point $(2,2)$ into the point-slope form of a line.
$y -2 =0.1(x -2)$

STEP 8

istribute the slope on the right side of the equation.
$y -2 =0.1x -0.2$

STEP 9

Add2 to both sides of the equation to solve for $y$ .
$y =.x -.2 +2$

STEP 10

implify the equation to find the equation of line $\ell$ .
$y =0.x +.8$ The equation of line $\ell$ is $y =0.x +.8$ .

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