Select the correct answer.

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

A. [tex]-\frac{4}{3}[/tex]
B. [tex]-\frac{3}{4}[/tex]
C. [tex]\frac{3}{4}[/tex]
D. [tex]\frac{4}{3}[/tex]



Answer :

Sure! Let's find the slope of the line passing through the points [tex]\((-4, 1)\)[/tex] and [tex]\((4, -5)\)[/tex].

The slope [tex]\(m\)[/tex] of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by the formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

Given the points [tex]\((-4, 1)\)[/tex] and [tex]\((4, -5)\)[/tex], we can identify:
[tex]\[ (x_1, y_1) = (-4, 1) \][/tex]
[tex]\[ (x_2, y_2) = (4, -5) \][/tex]

Plug these values into the slope formula:
[tex]\[ m = \frac{-5 - 1}{4 - (-4)} = \frac{-5 - 1}{4 + 4} = \frac{-6}{8} \][/tex]

Simplify the fraction:
[tex]\[ m = \frac{-6}{8} = \frac{-3}{4} \][/tex]

Therefore, the slope of the line passing through these points is:
[tex]\[ -\frac{3}{4} \][/tex]

Thus, the correct answer is:
[tex]\[ \boxed{-\frac{3}{4}} \][/tex]