Answered

Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Mr. Shaw graphs the function [tex]f(x) = -5x + 2[/tex] for his class. The line contains the point [tex]\((-2, 12)\)[/tex]. What is the point-slope form of the equation of the line he graphed?

[tex]\[
\begin{array}{l}
A. \ y - 12 = -5(x + 2) \\
B. \ y - 12 = 2(x + 2) \\
C. \ y + 12 = 2(x - 2) \\
D. \ y + 12 = -5(x - 2)
\end{array}
\][/tex]

Sagot :

GinnyAnswer
To find the point-slope form of the equation of the line, we need to use the following form:

[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.

Given:
- The slope of the line, [tex]\( m = -5 \)[/tex]
- The point on the line, [tex]\( (-2, 12) \)[/tex]

Let's substitute these values into the point-slope form equation.

1. Identify the point [tex]\( (x_1, y_1) \)[/tex]:
[tex]\[ (x_1, y_1) = (-2, 12) \][/tex]

2. Substitute [tex]\( x_1 = -2 \)[/tex], [tex]\( y_1 = 12 \)[/tex], and [tex]\( m = -5 \)[/tex] into the point-slope form equation:
[tex]\[ y - 12 = -5(x + 2) \][/tex]

Therefore, the point-slope form of the equation of the line Mr. Shaw graphed is:

[tex]\[ y - 12 = -5(x + 2) \][/tex]

Thus, the correct answer is:

[tex]\[ y - 12 = -5(x + 2) \][/tex]
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.