Question

The slope of this line is 1. Which of the following options shows how to correctly calculate the slope? Enter the number of the option that has calculated the slope correctly.Option #1: 0−32−5=−3−3=1 Option #2: 5−32−0=22=1 Option #3: 5−23−0=33=

Answer 1

To correctly calculate the slope of a line using two points \((x_1, y_1)\) and \((x_2, y_2)\), the formula is:

\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Now, let's evaluate each option to see which one correctly calculates the slope and equals 1.

### Option #1:
Given two points, we can interpret them as \((x_1, y_1) = (2, 3)\) and \((x_2, y_2) = (0, -5)\).
\[
\text{slope} = \frac{-5 - 3}{0 - 2} = \frac{-8}{-2} = 4 \quad \text{(not 1)}
\]

### Option #2:
Assuming the points are \((x_1, y_1) = (2, 0)\) and \((x_2, y_2) = (5, 3)\).
\[
\text{slope} = \frac{3 - 0}{5 - 2} = \frac{3}{3} = 1 \quad \text{(correct)}
\]

### Option #3:
Assuming the points are \((x_1, y_1) = (0, 2)\) and \((x_2, y_2) = (3, 5)\).
\[
\text{slope} = \frac{5 - 2}{3 - 0} = \frac{3}{3} = 1 \quad \text{(also correct)}
\]

Both Option #2 and Option #3 correctly calculate the slope as 1. If you need to choose just one option, you should enter **2** or **3**, as both yield the correct slope of 1.