Sure, let's find the slope of the line that passes through the points [tex]\((2, -5)\)[/tex] and [tex]\((7, 1)\)[/tex].
Here's the detailed, step-by-step solution:
### Step 1: Identify the coordinates of the points
We are given two points:
- Point 1: [tex]\((x_1, y_1) = (2, -5)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (7, 1)\)[/tex]
### Step 2: Recall the formula for the slope of a line
The slope [tex]\(m\)[/tex] of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
### Step 3: Substitute the coordinates into the formula
Substitute the coordinates [tex]\((2, -5)\)[/tex] and [tex]\((7, 1)\)[/tex] into the formula:
[tex]\[
m = \frac{1 - (-5)}{7 - 2}
\][/tex]
### Step 4: Simplify the numerator and the denominator
Simplify the expression in the numerator and the denominator:
[tex]\[
m = \frac{1 + 5}{7 - 2}
\][/tex]
[tex]\[
m = \frac{6}{5}
\][/tex]
### Step 5: Perform the division
Divide the numerator by the denominator to find the slope:
[tex]\[
m = 1.2
\][/tex]
So, the slope of the line that passes through the points [tex]\((2, -5)\)[/tex] and [tex]\((7, 1)\)[/tex] is [tex]\(1.2\)[/tex].
