Question

1. find the slope in the table.

x	y
6	6
9	8
12	10

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 from the table

Let's take the first two points \((3, 4)\) and \((6, 6)\), where \( x_1 = 3 \), \( y_1 = 4 \), \( x_2 = 6 \), \( y_2 = 6 \).

Step3: Calculate the slope

Substitute into the formula: \( m=\frac{6 - 4}{6 - 3}=\frac{2}{3} \).

We can verify with another pair, say \((6, 6)\) and \((9, 8)\): \( m=\frac{8 - 6}{9 - 6}=\frac{2}{3} \). And with \((9, 8)\) and \((12, 10)\): \( m=\frac{10 - 8}{12 - 9}=\frac{2}{3} \). So the slope is consistent.

Answer:

\(\frac{2}{3}\)