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.
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.
Answers
GPT-4o mini
To find the slope of the line that passes through the given points, we can calculate the slope using two of the points from the table. The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Let's take the first two points from the table:
Point 1: \((30, 45)\) and Point 2: \((33, 33)\).
Using these points:
\[
x_1 = 30, \quad y_1 = 45, \quad x_2 = 33, \quad y_2 = 33
\]
Now, substitute these values into the slope formula:
\[
m = \frac{33 - 45}{33 - 30} = \frac{-12}{3} = -4
\]
Therefore, the slope of the line is \(\boxed{-4}\).
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Let's take the first two points from the table:
Point 1: \((30, 45)\) and Point 2: \((33, 33)\).
Using these points:
\[
x_1 = 30, \quad y_1 = 45, \quad x_2 = 33, \quad y_2 = 33
\]
Now, substitute these values into the slope formula:
\[
m = \frac{33 - 45}{33 - 30} = \frac{-12}{3} = -4
\]
Therefore, the slope of the line is \(\boxed{-4}\).