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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]
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