Question

a line passes through the points in this table.

x | y
30 | 45
33 | 33
36 | 21
39 | 9

what is the slope of the line?
write your answer as an integer or simplified fraction.

Explanation:

Step1: Recall the 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 \( (30, 45) \) and \( (33, 33) \). Here, \( x_1 = 30 \), \( y_1 = 45 \), \( x_2 = 33 \), \( y_2 = 33 \).

Step3: Calculate the slope

Substitute the values into the slope formula:
\( m=\frac{33 - 45}{33 - 30}=\frac{- 12}{3}=- 4 \)

We can verify with another pair of points, say \( (33, 33) \) and \( (36, 21) \). Then \( x_1 = 33 \), \( y_1 = 33 \), \( x_2 = 36 \), \( y_2 = 21 \).
\( m=\frac{21 - 33}{36 - 33}=\frac{-12}{3}=-4 \). The slope is consistent.

Answer:

\(-4\)