To find the point-slope equation of a line with a given slope that passes through a specific point, we use the point-slope form of the equation of a line, which is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\( m \)[/tex] is the slope of the line and [tex]\( (x_1, y_1) \)[/tex] is the given point on the line.
Given:
- The slope [tex]\( m = -4 \)[/tex]
- The point [tex]\( (x_1, y_1) = (-2, 7) \)[/tex]
Substitute the given slope and point into the point-slope form equation:
[tex]\[ y - 7 = -4(x - (-2)) \][/tex]
Simplify the expression inside the parentheses:
[tex]\[ y - 7 = -4(x + 2) \][/tex]
Thus, the correct point-slope equation for the line is:
[tex]\[ y - 7 = -4(x + 2) \][/tex]
Looking at the given options:
A. [tex]\( y + 7 = -4(x + 2) \)[/tex]
B. [tex]\( y - 7 = -4(x - 2) \)[/tex]
C. [tex]\( y - 7 = -4(x + 2) \)[/tex]
D. [tex]\( y + 7 = -4(x - 2) \)[/tex]
The correct option is:
C. [tex]\( y - 7 = -4(x + 2) \)[/tex]
