Question

find the slope of each line
1)
slope = ______
2)
slope = ______
3)
slope = ______
4)
slope = ______
5)
slope = ______
6)
slope = ______
7)
slope = ______
8)
slope = ______

Explanation:

Step1: Recall Slope Formula

The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For a line on a grid, we can use "rise over run" (change in \( y \) divided by change in \( x \)).

Step2: Analyze Line 1

• Pick two points on the line. Let's take \((-4, 2)\) and \((4, 4)\) (approximate from the grid).
• Rise (change in \( y \)): \( 4 - 2 = 2 \)
• Run (change in \( x \)): \( 4 - (-4) = 8 \)
• Slope: \( \frac{2}{8}=\frac{1}{4} \)

Step3: Analyze Line 2

• Points: \((-4, -2)\) and \((4, -1)\)
• Rise: \( -1 - (-2)=1 \)
• Run: \( 4 - (-4)=8 \)
• Slope: \( \frac{1}{8} \)

Step4: Analyze Line 3

• Points: \((1, 4)\) and \((3, -4)\)
• Rise: \( -4 - 4=-8 \)
• Run: \( 3 - 1 = 2 \)
• Slope: \( \frac{-8}{2}=-4 \)

Step5: Analyze Line 4

• Vertical line (undefined slope, since run = 0, division by zero). But from grid, it's a vertical line, so slope is undefined (or "no slope").

Step6: Analyze Line 5

• Points: \((-4, 3)\) and \((4, 4)\)
• Rise: \( 4 - 3 = 1 \)
• Run: \( 4 - (-4)=8 \)
• Slope: \( \frac{1}{8} \)? Wait, recheck. Maybe better points: \((-8, 2)\) and \((8, 4)\). Rise: 2, Run: 16, slope \( \frac{2}{16}=\frac{1}{8} \)? Wait, original grid: Let's take \((-4, 3)\) and \((4, 4)\): rise 1, run 8, slope \( \frac{1}{8} \)? Wait, maybe I made a mistake. Alternatively, for line 5, let's use (0,3) and (8,4): rise 1, run 8, slope \( \frac{1}{8} \)? No, wait, maybe line 5: let's take two clear points. Let's say ( - 8, 2) and (8, 4). Then rise is 2, run is 16, slope \( \frac{2}{16} = \frac{1}{8} \)? Wait, maybe better to use (0,3) and (8,4): slope \( \frac{4 - 3}{8 - 0}=\frac{1}{8} \).

Step7: Analyze Line 6

• Points: \((-2, -4)\) and \((1, 2)\)
• Rise: \( 2 - (-4)=6 \)
• Run: \( 1 - (-2)=3 \)
• Slope: \( \frac{6}{3}=2 \)

Step8: Analyze Line 7

• Points: \((-2, -4)\) and \((2, 4)\)
• Rise: \( 4 - (-4)=8 \)
• Run: \( 2 - (-2)=4 \)
• Slope: \( \frac{8}{4}=2 \)

Step9: Analyze Line 8

• Points: \((-4, 3)\) and \((4, -1)\)
• Rise: \( -1 - 3=-4 \)
• Run: \( 4 - (-4)=8 \)
• Slope: \( \frac{-4}{8}=-\frac{1}{2} \)

Answer:

1. \(\frac{1}{4}\)
2. \(\frac{1}{8}\)
3. \(-4\)
4. Undefined
5. \(\frac{1}{8}\) (or recheck for accuracy)
6. \(2\)
7. \(2\)
8. \(-\frac{1}{2}\)

(Note: Some slopes may need re - checking with more precise grid points, but the above follows the "rise over run" method for each line.)