Question

1. the ordered pairs represent a linear relationship. what is the slope of the line?

x	y
-3	-18
-1	-8
0	-3
2	7
5	22

1. what is the slope of the line that passes through the points (-1, 8) and (3, 11)? express your answer as a fraction in simplest form.

1. what is the slope of the linear relationship represented by the table?

x	y
-5	16
-2	7
1	-2
3	-8
7	-20

Explanation:

Problem 3:

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, e.g., \((-3, -18)\) and \((-1, -8)\).

Step2: Substitute into formula

\( x_1=-3, y_1 = -18, x_2=-1, y_2=-8 \). Then \( m=\frac{-8 - (-18)}{-1 - (-3)}=\frac{-8 + 18}{-1 + 3}=\frac{10}{2}=5 \). Let's check with another pair, say \((0, -3)\) and \((2, 7)\): \( m=\frac{7 - (-3)}{2 - 0}=\frac{10}{2}=5 \). Consistent.

Step1: Identify points

Points are \((-1, 8)\) and \((3, 11)\). Let \( (x_1, y_1)=(-1, 8) \), \( (x_2, y_2)=(3, 11) \).

Step2: Apply slope formula

\( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{11 - 8}{3 - (-1)}=\frac{3}{4} \).

Step1: Select two points

Take \((-5, 16)\) and \((-2, 7)\). Let \( x_1=-5, y_1 = 16, x_2=-2, y_2=7 \).

Step2: Calculate slope

\( m=\frac{7 - 16}{-2 - (-5)}=\frac{-9}{3}=-3 \). Check with \((1, -2)\) and \((3, -8)\): \( m=\frac{-8 - (-2)}{3 - 1}=\frac{-6}{2}=-3 \). Consistent.

Answer:

5

Problem 5: