A line passes through the points in this table.

Question

x,y
(3,25)
(4,22)
(5,19)
(6,16)
What is the slope of the line?
Write your answer as an integer or simplified fraction.

Answer 1

To calculate the slope of a line given two points, the formula for 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 choose the first two points from the table: \( (3, 25) \) and \( (4, 22) \).

1. Identify the coordinates:

   • \( (x_1, y_1) = (3, 25) \)
   • \( (x_2, y_2) = (4, 22) \)

2. Substitute the values into the slope formula: \[ m = \frac{22 - 25}{4 - 3} = \frac{-3}{1} = -3 \]

Now, let's verify by using the second and third points: \( (4, 22) \) and \( (5, 19) \).

1. Identify the coordinates:

   • \( (x_1, y_1) = (4, 22) \)
   • \( (x_2, y_2) = (5, 19) \)

2. Substitute the values into the slope formula: \[ m = \frac{19 - 22}{5 - 4} = \frac{-3}{1} = -3 \]

Now, let's check the third and fourth points: \( (5, 19) \) and \( (6, 16) \).

1. Identify the coordinates:

   • \( (x_1, y_1) = (5, 19) \)
   • \( (x_2, y_2) = (6, 16) \)

2. Substitute the values into the slope formula: \[ m = \frac{16 - 19}{6 - 5} = \frac{-3}{1} = -3 \]

Since the slope remains consistent across all points, we can conclude that the slope of the line is:

\[ \boxed{-3} \]