Answered

Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Which equation represents a line that passes through [tex]$(-9,-3)$[/tex] and has a slope of -6?

A. [tex]y - 9 = -6(x - 3)[/tex]
B. [tex]y + 9 = -6(x + 3)[/tex]
C. [tex]y - 3 = -6(x - 9)[/tex]
D. [tex]y + 3 = -6(x + 9)[/tex]

Sagot :

GinnyAnswer
To find the equation of a line that passes through the point \((-9, -3)\) and has a slope of \(-6\), we can use the point-slope form of the equation of a line. The point-slope form is given by:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

where \((x_1, y_1)\) is a point on the line, and \(m\) is the slope.

Given:
- Point \((x_1, y_1) = (-9, -3)\)
- Slope \(m = -6\)

Substituting these values into the point-slope form, we get:

[tex]\[ y - (-3) = -6(x - (-9)) \][/tex]

Simplify the equation:
[tex]\[ y + 3 = -6(x + 9) \][/tex]

So, the equation of the line in point-slope form that passes through \((-9, -3)\) with a slope of \(-6\) is:

[tex]\[ y + 3 = -6(x + 9) \][/tex]

Now, let's match this equation with the given options:

1. \( y - 9 = -6(x - 3) \)
2. \( y + 9 = -6(x + 3) \)
3. \( y - 3 = -6(x - 9) \)
4. \( y + 3 = -6(x + 9) \)

The equation \( y + 3 = -6(x + 9) \) matches option 4.

Therefore, the equation that represents a line passing through \((-9, -3)\) and having a slope of \(-6\) is:

[tex]\[ \boxed{y + 3 = -6(x + 9)} \][/tex]

Thus, the correct option is 4
f4shore

__________________________________________________________

Hello! In this question, we are trying to figure out which equation represents the line that follows the given parameters.

__________________________________________________________

Explanation:

We are given the following information:

  • Line passes through the point (-9, -3)
  • Slope of -6

We also need to find our answer using the point-slope equation, as the answer choices follow this format:

y - y1 = m(x - x1)

Where:

  • m = slope
  • (x1, y1) is the coordinate point

__________________________________________________________

Solve:

Using the given information, we are able to solve the question.

We know that our slope is -6, which is m in our formula, so we could plug -6 into m to get closer to our answer:

y - y1 = -6(x - x1)

Now, since we know our coordinate point is (-9, -3), we can plug in our coordinate into the corresponding variable to complete our equation:

y - (-3) = -6(x - (-9))

Simplify:

y + 3 = -6(x + 9)

Therefore, this equation matches with answer choice D). y + 3 = -6(x + 9)

__________________________________________________________

Answer:

D). y + 3 = -6(x + 9)

__________________________________________________________

We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.