To find the slope of the line that passes through the points \((2, -5)\) and \((7, 1)\), we'll follow these steps:
Step 1: Choose \((x_1, y_1)\)
We can choose \((x_1, y_1) = (2, -5)\).
[tex]\[
x_1 = 2, \quad y_1 = -5
\][/tex]
Step 2: Choose \((x_2, y_2)\)
We can choose \((x_2, y_2) = (7, 1)\).
[tex]\[
x_2 = 7, \quad y_2 = 1
\][/tex]
Step 3: Apply the formula for the slope of a line
The slope \(m\) of a line that passes through points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Step 4: Substitute the values into the formula
[tex]\[
m = \frac{1 - (-5)}{7 - 2}
\][/tex]
Step 5: Simplify the expression
[tex]\[
m = \frac{1 + 5}{7 - 2} = \frac{6}{5} = 1.2
\][/tex]
So, the slope of the line that passes through the points [tex]\((2, -5)\)[/tex] and [tex]\((7, 1)\)[/tex] is 1.2.
