The image contains four problems and one bonus problem related to finding the slope of a line. Problem 1: Find the slope of the line given a table of points: $x = -1, 2, 5, 8$ and $y = 3, -1, -5, -9$. Problem 2: Find the slope of the line given a table of points: $x = 2, 8, 13$ and $y = -1, 0, 1$. Problem 3: Find the slope of the line passing through the points G$(-1, 2)$ and H$(7, 2)$. Problem 4: Find the slope of the line passing through the points F$(6, 8)$ and f$(6, -2)$. Bonus Problem: A student calculates the slope of the line passing through the points $(-3, 8)$ and $(2, -4)$ as $m = \frac{-3-8}{2-(-4)} = \frac{-11}{6}$. Identify the mistake and correct it.

1. Problem Description

The image contains four problems and one bonus problem related to finding the slope of a line.

Problem 1: Find the slope of the line given a table of points: $x = -1, 2, 5, 8$ and $y = 3, -1, -5, -9$.

Problem 2: Find the slope of the line given a table of points: $x = 2, 8, 13$ and $y = -1, 0, 1$.

Problem 3: Find the slope of the line passing through the points G$(-1, 2)$ and H$(7, 2)$.

Problem 4: Find the slope of the line passing through the points F$(6, 8)$ and f$(6, -2)$.

Bonus Problem: A student calculates the slope of the line passing through the points $(-3, 8)$ and $(2, -4)$ as $m = \frac{-3-8}{2-(-4)} = \frac{-11}{6}$. Identify the mistake and correct it.

2. Solution Steps

Problem 1:

We can use any two points from the table to find the slope. Let's use the first two points: $(-1, 3)$ and $(2, -1)$.

The formula for slope is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{-1 - 3}{2 - (-1)} = \frac{-4}{3}$

Problem 2:

Using the first two points: $(2, -1)$ and $(8, 0)$.

$m = \frac{0 - (-1)}{8 - 2} = \frac{1}{6}$

Problem 3:

Given points G$(-1, 2)$ and H$(7, 2)$.

$m = \frac{2 - 2}{7 - (-1)} = \frac{0}{8} = 0$

Problem 4:

Given points F$(6, 8)$ and f$(6, -2)$.

$m = \frac{-2 - 8}{6 - 6} = \frac{-10}{0}$

The slope is undefined since division by zero is not allowed.

Bonus Problem:

The student incorrectly substituted the x-coordinates for the y-coordinates in the numerator. The correct formula for slope is $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Using the points $(-3, 8)$ and $(2, -4)$:

$m = \frac{-4 - 8}{2 - (-3)} = \frac{-12}{5}$

3. Final Answer

Problem 1: $m = -\frac{4}{3}$

Problem 2: $m = \frac{1}{6}$

Problem 3: $m = 0$

Problem 4: Undefined

Bonus Problem: The mistake was incorrectly calculating the numerator. The correct slope is $m = -\frac{12}{5}$