Find the slopes of the linear functions.

Question

On a coordinate plane, a line goes through points (0, 6) and (6, 0). Y = negative 2 x + 7.

The slope of the line given by the linear equation is
.
The slope of the line shown in the graph is

Answer 1

To find the slopes of the linear functions given, let's analyze both the points and the equation provided.

1. Slope from the graph using points (0, 6) and (6, 0): The slope \( m \) can be calculated using the formula:

   \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

   Here, let's assign the points:

   • Point 1: \( (x_1, y_1) = (0, 6) \)
   • Point 2: \( (x_2, y_2) = (6, 0) \)

   Substituting these values into the slope formula:

   \[ m = \frac{0 - 6}{6 - 0} = \frac{-6}{6} = -1 \]

   So, the slope of the line shown in the graph is -1.

2. Slope from the linear equation \( Y = -2x + 7 \): In the equation of the line in the slope-intercept form \( Y = mx + b \), the coefficient \( m \) represents the slope.

   Here, the equation is: \[ Y = -2x + 7 \]

   Thus, the slope \( m \) from this equation is -2.

In summary:

• The slope of the line given by the linear equation is -2.
• The slope of the line shown in the graph is -1.