What is the slope of the line that contains the points [tex][tex]$(-1,2)$[/tex][/tex] and [tex][tex]$(4,3)$[/tex][/tex]?

A. -5
B. [tex][tex]$-\frac{1}{5}$[/tex][/tex]
C. [tex][tex]$\frac{1}{5}$[/tex][/tex]
D. 5



Answer :

To determine the slope of the line that passes through the points [tex]\((-1, 2)\)[/tex] and [tex]\( (4, 3) \)[/tex], we can use the slope formula:

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

Now let's identify our points:
- [tex]\((x_1, y_1) = (-1, 2)\)[/tex]
- [tex]\((x_2, y_2) = (4, 3)\)[/tex]

Plug these values into the slope formula:

[tex]\[ \text{slope} = \frac{3 - 2}{4 - (-1)} \][/tex]

Simplify the numerator and the denominator:

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

[tex]\[ \text{slope} = \frac{1}{5} \][/tex]

Therefore, the slope of the line that contains the points [tex]\((-1, 2)\)[/tex] and [tex]\( (4, 3) \)[/tex] is [tex]\(\frac{1}{5}\)[/tex], which corresponds to option C.

So, the correct answer is:
C. [tex]\(\frac{1}{5}\)[/tex]