Answer :
To determine the slope of the line given by the equation [tex]\( y + 2 = -3(x - 5) \)[/tex], we need to recognize that this equation is in the point-slope form.
The point-slope form of a linear equation is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\( m \)[/tex] is the slope, and [tex]\((x_1, y_1)\)[/tex] is a point on the line.
In the equation [tex]\( y + 2 = -3(x - 5) \)[/tex], we can compare it directly to the point-slope form. Here are the components:
- [tex]\( y_1 = -2 \)[/tex] (since [tex]\( y + 2 \)[/tex] can be rewritten as [tex]\( y - (-2) \)[/tex])
- [tex]\( x_1 = 5 \)[/tex] (since [tex]\( x - 5 \)[/tex] matches the form exactly).
The slope [tex]\( m \)[/tex] is the coefficient of [tex]\((x - x_1)\)[/tex], which in this case is [tex]\(-3\)[/tex].
Therefore, the slope of the line is:
[tex]\[ \boxed{-3} \][/tex]
The point-slope form of a linear equation is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\( m \)[/tex] is the slope, and [tex]\((x_1, y_1)\)[/tex] is a point on the line.
In the equation [tex]\( y + 2 = -3(x - 5) \)[/tex], we can compare it directly to the point-slope form. Here are the components:
- [tex]\( y_1 = -2 \)[/tex] (since [tex]\( y + 2 \)[/tex] can be rewritten as [tex]\( y - (-2) \)[/tex])
- [tex]\( x_1 = 5 \)[/tex] (since [tex]\( x - 5 \)[/tex] matches the form exactly).
The slope [tex]\( m \)[/tex] is the coefficient of [tex]\((x - x_1)\)[/tex], which in this case is [tex]\(-3\)[/tex].
Therefore, the slope of the line is:
[tex]\[ \boxed{-3} \][/tex]
