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

A. [tex]-\frac{5}{2}[/tex]
B. [tex]\frac{5}{2}[/tex]
C. [tex]\frac{2}{5}[/tex]
D. [tex]-\frac{2}{5}[/tex]



Answer :

To determine the slope of a line that contains the points \((-2, 2)\) and \((3, 4)\), we can use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

Here, \((x_1, y_1)\) and \((x_2, y_2)\) represent the coordinates of the given points.

First, identify the coordinates:
[tex]\[ x_1 = -2, \quad y_1 = 2, \quad x_2 = 3, \quad y_2 = 4 \][/tex]

Now, substitute these values into the slope formula:

[tex]\[ m = \frac{4 - 2}{3 - (-2)} \][/tex]

Calculate the numerator and the denominator separately:

[tex]\[ 4 - 2 = 2 \][/tex]

[tex]\[ 3 - (-2) = 3 + 2 = 5 \][/tex]

Now, substitute these results back into the slope formula:

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

Hence, the slope of the line containing the points \((-2, 2)\) and \((3, 4)\) is \(\frac{2}{5}\).

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