Answered

Get the information you need quickly and easily with IDNLearn.com. Ask your questions and receive comprehensive and trustworthy answers from our experienced community of professionals.

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 :

GinnyAnsweridn
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]
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.