Answer :
To find the slope of the line that passes through the points (2, -5) and (7, 1), we follow the steps below:
### Step 1: Choose [tex]\((x_1, y_1)\)[/tex]
Given points:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 2 & -5 \\ 7 & 1 \\ \hline \end{array} \][/tex]
Let's choose [tex]\((x_1, y_1)\)[/tex] as the first point.
[tex]\[ x_1 = 2, \; y_1 = -5 \][/tex]
### Step 2: Choose [tex]\((x_2, y_2)\)[/tex]
For the second point:
[tex]\[ x_2 = 7, \; y_2 = 1 \][/tex]
### Step 3: Use the slope formula
The formula to calculate the slope [tex]\(m\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
### Step 4: Substitute the values into the slope formula
Substitute [tex]\((x_1, y_1) = (2, -5)\)[/tex] and [tex]\((x_2, y_2) = (7, 1)\)[/tex] into the formula:
[tex]\[ m = \frac{1 - (-5)}{7 - 2} \][/tex]
### Step 5: Simplify the expression
First, simplify the numerator:
[tex]\[ 1 - (-5) = 1 + 5 = 6 \][/tex]
Next, simplify the denominator:
[tex]\[ 7 - 2 = 5 \][/tex]
Now, put it all together:
[tex]\[ m = \frac{6}{5} = 1.2 \][/tex]
### Conclusion
The slope of the line that passes through the points (2, -5) and (7, 1) is:
[tex]\[ \boxed{1.2} \][/tex]
### Step 1: Choose [tex]\((x_1, y_1)\)[/tex]
Given points:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 2 & -5 \\ 7 & 1 \\ \hline \end{array} \][/tex]
Let's choose [tex]\((x_1, y_1)\)[/tex] as the first point.
[tex]\[ x_1 = 2, \; y_1 = -5 \][/tex]
### Step 2: Choose [tex]\((x_2, y_2)\)[/tex]
For the second point:
[tex]\[ x_2 = 7, \; y_2 = 1 \][/tex]
### Step 3: Use the slope formula
The formula to calculate the slope [tex]\(m\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
### Step 4: Substitute the values into the slope formula
Substitute [tex]\((x_1, y_1) = (2, -5)\)[/tex] and [tex]\((x_2, y_2) = (7, 1)\)[/tex] into the formula:
[tex]\[ m = \frac{1 - (-5)}{7 - 2} \][/tex]
### Step 5: Simplify the expression
First, simplify the numerator:
[tex]\[ 1 - (-5) = 1 + 5 = 6 \][/tex]
Next, simplify the denominator:
[tex]\[ 7 - 2 = 5 \][/tex]
Now, put it all together:
[tex]\[ m = \frac{6}{5} = 1.2 \][/tex]
### Conclusion
The slope of the line that passes through the points (2, -5) and (7, 1) is:
[tex]\[ \boxed{1.2} \][/tex]
