For all your questions, big or small, IDNLearn.com has the answers you need. Discover reliable and timely information on any topic from our network of knowledgeable professionals.

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]