Find the slope of the line that passes through the points [tex](2, -5)[/tex] and [tex](7, 1)[/tex].

Step 1: Choose [tex](x_1, y_1)[/tex].
[tex]x_1 = 2, y_1 = -5[/tex]

Step 2: Calculate the slope using the formula:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

where [tex](x_2, y_2) = (7, 1)[/tex].



Answer :

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.