The function provided is $f(x) = \frac{2}{3}x + 4$. Let's break down how to graph this step by step:

1. Identify the Slope and Y-Intercept

• Slope (m): $\frac{2}{3}$. This means for every 3 units you move right on the $x$-axis, the graph rises 2 units on the $y$-axis.
• Y-Intercept (b): 4. The graph crosses the $y$-axis at the point $(0, 4)$.

2. Plot the Y-Intercept

Start by plotting the point $(0, 4)$ on the graph.

3. Use the Slope to Find Another Point

From the $y$-intercept, use the slope:

• Move 3 units to the right ($+3$ on $x$) and 2 units up ($+2$ on $y$).
• This gives another point: $(3, 6)$.

4. Draw the Line

• Plot the second point, $(3, 6)$.
• Connect these points with a straight line and extend it in both directions.

You can also find a point in the opposite direction by moving 3 units to the left ($-3$ on $x$) and 2 units down ($-2$ on $y$). This gives the point $(-3, 2)$.

Would you like me to graph this function for you or provide more details?

5 Related Questions

1. How would you determine the slope of a line from its equation in standard form?
2. What is the significance of the y-intercept in real-world applications?
3. How do you find the x-intercept of the line $f(x) = \frac{2}{3}x + 4$?
4. What happens to the graph if the slope changes to $-\frac{2}{3}$?
5. How do you graph a vertical or horizontal line?

Tip:

Always verify at least two points when graphing a line to ensure accuracy.