The equation given is $f(x) = 4x - 2$, which represents a linear function.

Steps to graph this:

1. Identify the slope and y-intercept:

   • The equation is in the slope-intercept form $y = mx + b$, where:
     • $m = 4$ is the slope.
     • $b = -2$ is the y-intercept.

2. Plot the y-intercept:

   • The point where the line crosses the y-axis is at $(0, -2)$.

3. Use the slope to find other points:

   • The slope $m = 4$ means that for every 1 unit increase in $x$, $y$ increases by 4 units.
   • Starting at $(0, -2)$, if you move 1 unit to the right (x = 1), the y-value increases by 4, so the next point is $(1, 2)$.

4. Plot additional points using the slope:

   • From $(1, 2)$, move right by 1 unit again, and up 4 more units, so another point is $(2, 6)$.

5. Draw the line:

   • Connect these points with a straight line, extending the line in both directions.

Would you like a step-by-step graph illustration of this? Let me know if you have any questions or need further details.

Related questions:

1. What is the general form of a linear equation and how does it compare to the slope-intercept form?
2. How do you interpret the slope geometrically on a graph?
3. What does the y-intercept represent in real-life situations?
4. How do you find the x-intercept from a linear equation?
5. What is the relationship between the slope and the angle of the line?

Tip:

Always check the slope sign carefully. A positive slope means the line rises, while a negative slope means it falls.