To graph the given function and complete the missing table values, let’s proceed step by step.

The equation of the line:

$y = \frac{4}{3}x - 1$ Here:

• The slope $m = \frac{4}{3}$,
• The y-intercept $b = -1$.

1. Fill in the missing $y$-values in the table:

To calculate $y$-values, substitute $x$-values into the equation $y = \frac{4}{3}x - 1$.

• When $x = -3$: $y = \frac{4}{3}(-3) - 1 = -4 - 1 = -5$
• When $x = 0$: $y = \frac{4}{3}(0) - 1 = -1$
• When $x = 3$: $y = \frac{4}{3}(3) - 1 = 4 - 1 = 3$
• When $x = 6$: $y = \frac{4}{3}(6) - 1 = 8 - 1 = 7$

2. The completed table:

3. Plot the points:

Plot the following points on the graph:

1. $(-3, -5)$
2. $(0, -1)$
3. $(3, 3)$
4. $(6, 7)$

These points should form a straight line because the equation is linear.

4. Draw the line:

• Start at the y-intercept $(0, -1)$,
• Use the slope $\frac{4}{3}$: move 4 units up and 3 units to the right to plot additional points.

Would you like me to explain more about graphing or clarify the steps? Let me know!

Related Questions:

1. How do you determine the slope of a line from its equation?
2. What is the significance of the y-intercept in a linear function?
3. How can you verify if two points lie on the same straight line?
4. How would the graph change if the slope were negative?
5. What is the equation of a line parallel to $y = \frac{4}{3}x - 1$?

Tip: To graph lines with a fractional slope, always move vertically (numerator) and horizontally (denominator).