QuestionConsider the following lines. Line 1: $3 x-4 y=12$ Line 2: a line perpendicular to $3 x-4 y=12$ that contains the point $(3,-4)$ Write the equation of Line 1 in slope-intercept form. $\square$ Find the slope of Line 1. $\square$

Studdy Solution

STEP 1

1. Line 1 is given in standard form, and we need to convert it to slope-intercept form.
2. The slope-intercept form of a line is given by $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
3. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.

STEP 2

1. Convert the equation of Line 1 from standard form to slope-intercept form.
2. Determine the slope of Line 1 from the slope-intercept form.

STEP 3

Start with the equation of Line 1 in standard form:
$3x - 4y = 12$
Solve for $y$ to convert it to slope-intercept form. First, isolate the term with $y$ :
$-4y = -3x + 12$

STEP 4

Divide each term by $-4$ to solve for $y$ :
$y = \frac{3}{4}x - 3$
Now, the equation is in slope-intercept form, where the slope $m$ is $\frac{3}{4}$ and the y-intercept $b$ is $-3$ .

STEP 5

Identify the slope of Line 1 from the slope-intercept form:
The slope $m$ of Line 1 is $\frac{3}{4}$ .
The equation of Line 1 in slope-intercept form is:
$y = \frac{3}{4}x - 3$
The slope of Line 1 is:
$\frac{3}{4}$

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