Answer :
To determine the slope of the equation [tex]\( y - 3 = -4(x - 5) \)[/tex], we can identify the form of the equation presented.
The equation [tex]\( y - 3 = -4(x - 5) \)[/tex] is written in the point-slope form of a linear equation, which is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Here, [tex]\( (x_1, y_1) \)[/tex] is a specific point on the line, and [tex]\( m \)[/tex] represents the slope of the line.
By comparing the given equation [tex]\( y - 3 = -4(x - 5) \)[/tex] with the general point-slope form [tex]\( y - y_1 = m(x - x_1) \)[/tex], we can identify the components:
- [tex]\( y_1 = 3 \)[/tex]
- [tex]\( x_1 = 5 \)[/tex]
- [tex]\( m = -4 \)[/tex]
The slope [tex]\( m \)[/tex] is the coefficient of [tex]\( (x - x_1) \)[/tex], which in this case is -4.
Therefore, the slope of the equation [tex]\( y - 3 = -4(x - 5) \)[/tex] is:
[tex]\[ -4 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{-4} \][/tex]
The equation [tex]\( y - 3 = -4(x - 5) \)[/tex] is written in the point-slope form of a linear equation, which is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Here, [tex]\( (x_1, y_1) \)[/tex] is a specific point on the line, and [tex]\( m \)[/tex] represents the slope of the line.
By comparing the given equation [tex]\( y - 3 = -4(x - 5) \)[/tex] with the general point-slope form [tex]\( y - y_1 = m(x - x_1) \)[/tex], we can identify the components:
- [tex]\( y_1 = 3 \)[/tex]
- [tex]\( x_1 = 5 \)[/tex]
- [tex]\( m = -4 \)[/tex]
The slope [tex]\( m \)[/tex] is the coefficient of [tex]\( (x - x_1) \)[/tex], which in this case is -4.
Therefore, the slope of the equation [tex]\( y - 3 = -4(x - 5) \)[/tex] is:
[tex]\[ -4 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{-4} \][/tex]
