Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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

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

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


Sagot :

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]