To find the slope of the line that goes through the points [tex]$(1, -5)$[/tex] and [tex]$(4, 1)$[/tex], we can use the formula for the slope of a line given two points \((x_1, y_1)\) and \((x_2, y_2)\). The formula for the slope \(m\) is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, our points are \((1, -5)\) and \((4, 1)\). Let's substitute these points into the formula:
1. Identify the coordinates:
[tex]\[
x_1 = 1, \quad y_1 = -5, \quad x_2 = 4, \quad y_2 = 1
\][/tex]
2. Substitute the coordinates into the slope formula:
[tex]\[
m = \frac{1 - (-5)}{4 - 1}
\][/tex]
3. Simplify the numerator and the denominator:
[tex]\[
m = \frac{1 + 5}{4 - 1} = \frac{6}{3}
\][/tex]
4. Divide the numerator by the denominator:
[tex]\[
m = \frac{6}{3} = 2
\][/tex]
Thus, the slope of the line that goes through the points [tex]$(1, -5)$[/tex] and [tex]$(4, 1)$[/tex] is \(2\).
The correct answer is:
D. 2
