Answered

Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

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

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 determine which equation represents the line that passes through the point [tex]\((-9, -3)\)[/tex] and has a slope of [tex]\(-6\)[/tex], 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 [tex]\((x_1, y_1)\)[/tex] is a point on the line and [tex]\(m\)[/tex] is the slope.

Given:
[tex]\( (x_1, y_1) = (-9, -3) \)[/tex]
[tex]\( m = -6 \)[/tex]

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

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

This simplifies to:
[tex]\[ y + 3 = -6(x + 9) \][/tex]

So, the equation that represents the line passing through the point [tex]\((-9, -3)\)[/tex] with a slope of [tex]\(-6\)[/tex] is:

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

Among the given options, this corresponds to:

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

Thus, the correct equation is:

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

In the given multiple-choice format, the correct answer is the fourth option:

[tex]\[ y+3=-6(x+9) \][/tex]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.