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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]

Sagot :

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

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

Let's use the given points [tex]\((-4, 1)\)[/tex] and [tex]\((4, -5)\)[/tex]:

1. [tex]\(x_1 = -4\)[/tex], [tex]\(y_1 = 1\)[/tex]
2. [tex]\(x_2 = 4\)[/tex], [tex]\(y_2 = -5\)[/tex]

Substitute these values into the slope formula:

[tex]\[ m = \frac{-5 - 1}{4 - (-4)} \][/tex]

First, simplify the numerator:

[tex]\[ -5 - 1 = -6 \][/tex]

Next, simplify the denominator:

[tex]\[ 4 - (-4) = 4 + 4 = 8 \][/tex]

Now we can calculate the slope:

[tex]\[ m = \frac{-6}{8} \][/tex]

Simplify the fraction:

[tex]\[ m = -\frac{6}{8} = -\frac{3}{4} \][/tex]

Therefore, the correct answer is:

[tex]\[ -\frac{3}{4} \][/tex]
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