Consider the following linear equation. \( f(x)=5 x-6 \)

The given linear equation is \( f(x) = 5x - 6 \). ### Known Conditions: - This is a linear function where: - The slope \( m = 5 \) - The y-intercept \( b = -6 \) ### Steps to Analyze the Function: 1. **Identify the Slope and Y-Intercept:** - The slope indicates that for every unit increase in \( x \), \( f(x) \) increases by 5. - The y-intercept tells us that the function crosses the y-axis at \( (0, -6) \). 2. **Determine the Function's Features:** - The function is linear, meaning it will graph as a straight line. - It has no maximum or minimum values since it extends infinitely in both directions. 3. **Find the x-Intercept:** - To find the x-intercept, set \( f(x) = 0 \): \[ 0 = 5x - 6 \] - Solve for \( x \): \[ 5x = 6 \implies x = \frac{6}{5} \] 4. **Graph the Function:** - The graph will have a slope of 5 and will cross the y-axis at -6 and the x-axis at \( \left(\frac{6}{5}, 0\right) \). If you need further analysis or specific calculations related to this function, please let me know!