What is the slope of the line that contains the points [tex]\((-2,2)\)[/tex] and [tex]\((3,4)\)[/tex]?

A. [tex]\(\frac{2}{5}\)[/tex]

B. [tex]\(\frac{5}{2}\)[/tex]

C. [tex]\(-\frac{5}{2}\)[/tex]

D. [tex]\(-\frac{2}{5}\)[/tex]



Answer :

To determine the slope of the line that passes through the points [tex]\((-2, 2)\)[/tex] and [tex]\( (3, 4)\)[/tex], we will use the slope formula:

[tex]\[ m = \frac{y2 - y1}{x2 - x1} \][/tex]

Here, [tex]\((x1, y1)\)[/tex] is [tex]\((-2, 2)\)[/tex] and [tex]\((x2, y2)\)[/tex] is [tex]\( (3, 4)\)[/tex]. Substituting these coordinates into the slope formula:

1. Calculate the numerator of the slope formula:
[tex]\[ y2 - y1 = 4 - 2 = 2 \][/tex]

2. Calculate the denominator of the slope formula:
[tex]\[ x2 - x1 = 3 - (-2) = 3 + 2 = 5 \][/tex]

3. Divide the numerator by the denominator to get the slope:
[tex]\[ m = \frac{2}{5} \][/tex]

Thus, the slope of the line that passes through the points [tex]\((-2, 2)\)[/tex] and [tex]\( (3, 4)\)[/tex] is:

[tex]\[ m = \frac{2}{5} \][/tex]

Therefore, the correct answer is:
A. [tex]\(\frac{2}{5}\)[/tex]