Function \( A \) is a linear function whose graph passes through the points \( (-5,-24) \) and \( (5,0) \). Below are the equations of three other linear functions. Sort the functions by their slopes. \( \frac{12}{5} x+y=3 \) Slope less than Function Slope equal to Function A's A's \( \frac{12}{5} x \quad 5 y-12 x=50 \) Slope greater than Function A's

To solve the problem, we need to determine the slope of Function \( A \) and the slopes of the other given functions. ### Step 1: Find the slope of Function \( A \) Function \( A \) is a linear function that passes through the points \( (-5, -24) \) and \( (5, 0) \). The slope \( m \) of a line through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the points into the formula: - \( (x_1, y_1) = (-5, -24) \) - \( (x_2, y_2) = (5, 0) \) Calculating the slope: \[ m_A = \frac{0 - (-24)}{5 - (-5)} = \frac{24}{10} = \frac{12}{5} \] ### Step 2: Find the slopes of the other functions 1. **For the equation \( \frac{12}{5} x + y = 3 \)**: Rearranging to slope-intercept form \( y = mx + b \): \[ y = -\frac{12}{5} x + 3 \] The slope \( m_1 = -\frac{12}{5} \). 2. **For the equation \( 5y - 12x = 50 \)**: Rearranging to slope-intercept form: \[ 5y = 12x + 50 \implies y = \frac{12}{5} x + 10 \] The slope \( m_2 = \frac{12}{5} \). 3. **For the equation \( A's \frac{12}{5} x \)**: This is the same as the slope of Function \( A \), which is \( m_A = \frac{12}{5} \). ### Step 3: Sort the slopes Now we have the slopes: - \( m_A = \frac{12}{5} \) - \( m_1 = -\frac{12}{5} \) - \( m_2 = \frac{12}{5} \) Sorting them: - Slope less than Function \( A \)'s: \( -\frac{12}{5} \) - Slope equal to Function \( A \)'s: \( \frac{12}{5} \) - Slope greater than Function \( A \)'s: (none, since there are no slopes greater than \( \frac{12}{5} \)) ### Final Result The sorted functions by their slopes are: - Slope less than Function \( A \)'s: \( \frac{12}{5} x + y = 3 \) (slope \( -\frac{12}{5} \)) - Slope equal to Function \( A \)'s: \( 5y - 12x = 50 \) (slope \( \frac{12}{5} \)) - Slope greater than Function \( A \)'s: None Thus, the final order is: 1. \( \frac{12}{5} x + y = 3 \) (slope \( -\frac{12}{5} \)) 2. \( 5y - 12x = 50 \) (slope \( \frac{12}{5} \))