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What is the slope of the line given by the equation below?

[tex]\[ y + 2 = -3(x - 5) \][/tex]

A. -5
B. 3
C. -3
D. 2


Sagot :

To determine the slope of the line given by the equation:

[tex]\[ y + 2 = -3(x - 5) \][/tex]

we need to compare it to the point-slope form of a linear equation, which is:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

In this form, [tex]\( m \)[/tex] represents the slope of the line, and [tex]\((x_1, y_1)\)[/tex] is a point on the line.

Looking at the given equation:

[tex]\[ y + 2 = -3(x - 5) \][/tex]

we can see that it fits the point-slope form [tex]\( y - y_1 = m(x - x_1) \)[/tex].

By comparing:

[tex]\[ y - y_1 = -3(x - x_1) \][/tex]

to the given equation [tex]\( y + 2 = -3(x - 5) \)[/tex], we identify that the slope [tex]\( m \)[/tex] is given by the coefficient of [tex]\((x - x_1)\)[/tex], which is [tex]\(-3\)[/tex].

Therefore, the slope [tex]\( m \)[/tex] is:

[tex]\[ \boxed{-3} \][/tex]

The correct answer is:

C. [tex]\(-3\)[/tex]