What is the slope of the line that goes through the points [tex]\((-4, 2)\)[/tex] and [tex]\((8, 5)\)[/tex]?

A. -4

B. [tex]\(-\frac{1}{4}\)[/tex]

C. [tex]\(\frac{1}{4}\)[/tex]

D. 4



Answer :

To determine the slope of the line that passes through the points [tex]\((-4, 2)\)[/tex] and [tex]\((8, 5)\)[/tex], we use the slope formula:

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

Here, [tex]\((x_1, y_1) = (-4, 2)\)[/tex] and [tex]\((x_2, y_2) = (8, 5)\)[/tex].

Plugging in these coordinates into the formula, we have:

[tex]\[ \text{slope} = \frac{5 - 2}{8 - (-4)} \][/tex]

Simplify the numerator and the denominator:

[tex]\[ \text{slope} = \frac{3}{8 + 4} \][/tex]

[tex]\[ \text{slope} = \frac{3}{12} \][/tex]

Simplify the fraction:

[tex]\[ \text{slope} = \frac{1}{4} \][/tex]

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

Thus, the correct answer is:

C. [tex]\(\frac{1}{4}\)[/tex]
The slope of the line is:
y2-y1/x2-x1

(8-(-4)/ (5-2)
(8+4) / 3
12/3
4

The answer is D.

The slope is 4.