Assignment 4.1 Slope/Rate of Change, Graphing on a coordinate plane Find the slope of the line from the two points given.

## Step 1: Understanding the Slope Formula<br />### The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:<br />\[<br />m = \frac{y_2 - y_1}{x_2 - x_1}<br />\]<br /><br />## Step 2: Calculating the Slope for Each Pair of Points<br /><br />### **1. Points (7, 1) and (8, 6):**<br />- \( x_1 = 7, y_1 = 1, x_2 = 8, y_2 = 6 \)<br />- Substitute into the formula:<br />\[<br />m = \frac{6 - 1}{8 - 7} = \frac{5}{1} = 5<br />\]<br /><br />### **2. Points (7, -3) and (10, -3):**<br />- \( x_1 = 7, y_1 = -3, x_2 = 10, y_2 = -3 \)<br />- Substitute into the formula:<br />\[<br />m = \frac{-3 - (-3)}{10 - 7} = \frac{0}{3} = 0<br />\]<br /><br />### **3. Points (-5, 20) and (-5, 16):**<br />- \( x_1 = -5, y_1 = 20, x_2 = -5, y_2 = 16 \)<br />- Substitute into the formula:<br />\[<br />m = \frac{16 - 20}{-5 - (-5)} = \frac{-4}{0}<br />\]<br />- Since division by zero is undefined, the slope is undefined. This indicates a vertical line.<br /><br />### **4. Points (1, 0) and (6, -3):**<br />- \( x_1 = 1, y_1 = 0, x_2 = 6, y_2 = -3 \)<br />- Substitute into the formula:<br />\[<br />m = \frac{-3 - 0}{6 - 1} = \frac{-3}{5}<br />\]