Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Choose the equation below that represents the line passing through the point [tex]\((-2, -3)\)[/tex] with a slope of -6.

A. [tex]\(y + 3 = -6(x + 2)\)[/tex]

B. [tex]\(y + 2 = 6(x + 3)\)[/tex]

C. [tex]\(y - 3 = -6(x - 2)\)[/tex]

D. [tex]\(y - 2 = 6(x - 3)\)[/tex]

Sagot :

GinnyAnswer
To determine which equation represents the line passing through the point [tex]\((-2, -3)\)[/tex] with a slope of [tex]\(-6\)[/tex], we can use the point-slope form of a linear equation. The point-slope form is given by:

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

where [tex]\((x_1, y_1)\)[/tex] is a point on the line, and [tex]\(m\)[/tex] is the slope of the line. Let's apply the given point [tex]\((-2, -3)\)[/tex] and the slope [tex]\(-6\)[/tex].

1. Substitute the given point and slope into the point-slope form:

[tex]\[ y - (-3) = -6(x - (-2)) \][/tex]

2. Simplify the equation:

[tex]\[ y + 3 = -6(x + 2) \][/tex]

Hence, the equation that represents the line passing through the point [tex]\((-2, -3)\)[/tex] with a slope of [tex]\(-6\)[/tex] is:

[tex]\[ y + 3 = -6(x + 2) \][/tex]

We can now match this equation with the given options:

1. [tex]\(y+3=-6(x+2)\)[/tex]
2. [tex]\(y+2=6(x+3)\)[/tex]
3. [tex]\(y-3=-6(x-2)\)[/tex]
4. [tex]\(y-2=6(x-3)\)[/tex]

The correct equation is option 1:

[tex]\[ y+3=-6(x+2) \][/tex]

Therefore, the answer is the first option.
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.