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]