Question

the points given in the table lie on a line. find the slope of each line. (example 1) 4.

x	0	2	4	6
y	9	4	-1	-6

5.

x	0	1	2	3
y	3	5	7	9

Explanation:

Problem 4:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take two points from the table, say \((0, 9)\) and \((2, 4)\).

Step2: Substitute into formula

\( x_1 = 0, y_1 = 9, x_2 = 2, y_2 = 4 \). So \( m=\frac{4 - 9}{2 - 0}=\frac{-5}{2}=-\frac{5}{2} \). We can check with another pair, like \((2, 4)\) and \((4, -1)\): \( \frac{-1 - 4}{4 - 2}=\frac{-5}{2} \), same result.

Step1: Use slope formula

Take two points, e.g., \((0, 3)\) and \((1, 5)\). The slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Substitute values

\( x_1 = 0, y_1 = 3, x_2 = 1, y_2 = 5 \). So \( m=\frac{5 - 3}{1 - 0}=\frac{2}{1}=2 \). Check with \((1, 5)\) and \((2, 7)\): \( \frac{7 - 5}{2 - 1}=2 \), consistent.

Answer:

\(-\frac{5}{2}\)

Problem 5: