Question

1. find the slope of the line that passes through all of the points on the table.

x	y
2	5
3	8
4	11

show your work here

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Choose two points

Let's take the first two points \((1, 2)\) and \((2, 5)\). Here, \( x_1 = 1 \), \( y_1 = 2 \), \( x_2 = 2 \), \( y_2 = 5 \).

Step3: Calculate slope

Substitute into the formula: \( m=\frac{5 - 2}{2 - 1}=\frac{3}{1}=3 \). We can check with other points (e.g., \((2,5)\) and \((3,8)\)): \( m=\frac{8 - 5}{3 - 2}=\frac{3}{1}=3 \), and \((3,8)\) and \((4,11)\): \( m=\frac{11 - 8}{4 - 3}=\frac{3}{1}=3 \), so the slope is consistent.

Answer:

3