High School

We appreciate your visit to Line tex L 1 tex has the following equation tex 7x 5y 10 tex Express the equation of tex L 1 tex in slope intercept. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Line [tex] L_1 [/tex] has the following equation: [tex]7x - 5y = -10[/tex]

Express the equation of [tex] L_1 [/tex] in slope-intercept form.

Answer :

To express the equation of line L1, which is given in the standard form [tex]\(7x - 5y = -10\)[/tex], in the slope-intercept form [tex]\(y = mx + b\)[/tex], follow these steps:

1. Isolate the term with [tex]\(y\)[/tex]:
Start by moving the [tex]\(7x\)[/tex] term to the other side of the equation by subtracting [tex]\(7x\)[/tex] from both sides:

[tex]\[
7x - 5y = -10 \quad \Rightarrow \quad -5y = -7x - 10
\][/tex]

2. Solve for [tex]\(y\)[/tex]:
Next, eliminate the coefficient of [tex]\(y\)[/tex] by dividing every term in the equation by [tex]\(-5\)[/tex]:

[tex]\[
-5y = -7x - 10 \quad \Rightarrow \quad y = \frac{-7}{-5}x + \frac{-10}{-5}
\][/tex]

Simplify the fractions:

[tex]\[
y = \frac{7}{5}x + 2
\][/tex]

Now, the equation is in the slope-intercept form [tex]\(y = mx + b\)[/tex], where:
- The slope [tex]\(m\)[/tex] is [tex]\(\frac{7}{5}\)[/tex].
- The [tex]\(y\)[/tex]-intercept [tex]\(b\)[/tex] is [tex]\(2\)[/tex].

So the slope-intercept form of the equation is [tex]\(y = \frac{7}{5}x + 2\)[/tex].

Thanks for taking the time to read Line tex L 1 tex has the following equation tex 7x 5y 10 tex Express the equation of tex L 1 tex in slope intercept. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada