Graph the function ​f(x)equals 5 x minus 7
. Calculus

To graph the function \( f(x) = 5x - 7 \), let's break down its components.

1. **Identify the Slope and Y-Intercept**:  
   - The function \( f(x) = 5x - 7 \) is in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
   - Here, \( m = 5 \) and \( b = -7 \).
   - This slope, \( m = 5 \), indicates that for every unit increase in \( x \), \( f(x) \) increases by 5 units.
   - The y-intercept \( b = -7 \) is the point where the line crosses the y-axis, at \( (0, -7) \).

2. **Plotting Points**:
   - Start by plotting the y-intercept at \( (0, -7) \).
   - Use the slope \( 5 \) (rise over run, or \( \frac{5}{1} \)) to find another point. From \( (0, -7) \), move up 5 units and right 1 unit to reach \( (1, -2) \).

3. **Drawing the Line**:
   - Connect these points to form a straight line.

Let me know if you'd like a visual plot of this, or have any further questions!

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### Further Related Questions
1. How do we interpret the slope in real-world applications?
2. What is the derivative of \( f(x) = 5x - 7 \) and what does it represent?
3. How would the graph change if the slope was negative?
4. Can we calculate the x-intercept of this function, and how?
5. What would happen if we added a constant to the function, like \( f(x) = 5x - 7 + c \)?

#### Tip
For any linear function \( f(x) = mx + b \), the slope \( m \) directly controls the line's steepness, while \( b \) sets its position along the y-axis.

Learn how to graph the linear function f(x) = 5x - 7, identifying the slope and y-intercept. This guide covers the slope-intercept form, plotting points, and drawing the line. Suitable for Grades 8-10 students learning linear equations and graphing concepts.

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