Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

A line passes through the point [tex]\((-1, -8)\)[/tex] and has a slope of [tex]\(-7\)[/tex].

Write an equation in slope-intercept form for this line.

[tex]\(\boxed{\ } \)[/tex]

Sagot :

GinnyAnswer
To find the equation of a line in slope-intercept form ([tex]\(y = mx + b\)[/tex]), we need two key pieces of information: the slope ([tex]\(m\)[/tex]) and the y-intercept ([tex]\(b\)[/tex]).

Given:
- The line passes through the point [tex]\((-1, -8)\)[/tex]
- The slope ([tex]\(m\)[/tex]) is [tex]\(-7\)[/tex]

We start by substituting the slope and the coordinates of the given point into the slope-intercept form equation to find the y-intercept ([tex]\(b\)[/tex]).

The general equation of a line in slope-intercept form is:
[tex]\[ y = mx + b \][/tex]

Substitute the slope [tex]\(-7\)[/tex] for [tex]\(m\)[/tex] and the coordinates of the point [tex]\((-1, -8)\)[/tex] for [tex]\(x\)[/tex] and [tex]\(y\)[/tex]:
[tex]\[ -8 = (-7)(-1) + b \][/tex]

Simplify the equation:
[tex]\[ -8 = 7 + b \][/tex]

To isolate [tex]\(b\)[/tex], subtract 7 from both sides:
[tex]\[ b = -8 - 7 \][/tex]
[tex]\[ b = -15 \][/tex]

Now, we have the slope ([tex]\(m = -7\)[/tex]) and the y-intercept ([tex]\(b = -15\)[/tex]). We can write the equation of the line in slope-intercept form:
[tex]\[ y = -7x - 15 \][/tex]

Therefore, our equation is:
[tex]\[ y = -7x - 15 \][/tex]
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.