Question

ll your work. then graph the line,

1. $f(x) = \frac{2}{3}x - 1$

Explanation:

Step1: Choose x values

Let's pick x values like -3, 0, 3, 6, -6, 9. These values will make the calculation of y (since the slope is 2/3) easier as they are multiples of 3.

Step2: Calculate y for x = -3

Substitute x = -3 into \( f(x)=\frac{2}{3}x - 1 \). So \( y=\frac{2}{3}(-3)-1=-2 - 1=-3 \).

Step3: Calculate y for x = 0

Substitute x = 0 into the function. \( y=\frac{2}{3}(0)-1 = 0 - 1=-1 \).

Step4: Calculate y for x = 3

Substitute x = 3. \( y=\frac{2}{3}(3)-1=2 - 1 = 1 \).

Step5: Calculate y for x = 6

Substitute x = 6. \( y=\frac{2}{3}(6)-1 = 4 - 1=3 \).

Step6: Calculate y for x = -6

Substitute x = -6. \( y=\frac{2}{3}(-6)-1=-4 - 1=-5 \).

Step7: Calculate y for x = 9

Substitute x = 9. \( y=\frac{2}{3}(9)-1 = 6 - 1=5 \).

Now the table will be:

x	y
-3	-3
0	-1
3	1
6	3
9	5

To graph the line, plot these points (-6, -5), (-3, -3), (0, -1), (3, 1), (6, 3), (9, 5) on the coordinate plane and draw a straight line through them. The y - intercept is -1 (from the point (0, -1)) and the slope is 2/3, which means for every 3 units we move to the right (increase x by 3), we move up 2 units (increase y by 2).

Answer:

The table is filled as above, and the line is graphed by plotting the points and drawing a straight line through them. The key points for the table are (x, y) pairs: (-6, -5), (-3, -3), (0, -1), (3, 1), (6, 3), (9, 5).