What is the slope of the line that contains the points [tex][tex]$(-1,8)$[/tex][/tex] and [tex][tex]$(5,-4)$[/tex][/tex]?

A. -2
B. 2
C. [tex][tex]$\frac{1}{2}$[/tex][/tex]
D. [tex][tex]$-\frac{1}{2}$[/tex][/tex]



Answer :

To find the slope of the line that contains the points [tex]\((-1, 8)\)[/tex] and [tex]\( (5, -4) \)[/tex], we use the slope formula:

[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

Substituting the coordinates of the given points into the formula where [tex]\((x_1, y_1) = (-1, 8)\)[/tex] and [tex]\((x_2, y_2) = (5, -4)\)[/tex]:

[tex]\[ \text{slope} = \frac{-4 - 8}{5 - (-1)} \][/tex]

Simplify the expressions in the numerator and the denominator:

[tex]\[ = \frac{-4 - 8}{5 + 1} \][/tex]

[tex]\[ = \frac{-12}{6} \][/tex]

Now, divide [tex]\(-12\)[/tex] by [tex]\(6\)[/tex]:

[tex]\[ = -2 \][/tex]

Therefore, the slope of the line that contains the points [tex]\((-1, 8)\)[/tex] and [tex]\( (5, -4) \)[/tex] is [tex]\(-2\)[/tex].

The correct answer is [tex]\(\boxed{-2}\)[/tex].