Below, fill in the table of values and use the table values to graph [tex]y=x-4[/tex].

| x | y=x-4 |
|---|---|
| -3 |
| -2 |
| -1 |
| 0 |
| 1 |
| 2 |
| 3 |

Substitute each x value into the equation y = x − 4 to find the corresponding y value.
Calculate y for x = − 3 , − 2 , − 1 , 0 , 1 , 2 , 3 .
Plot the points (-3, -7), (-2, -6), (-1, -5), (0, -4), (1, -3), (2, -2), and (3, -1) on a graph.
Draw a straight line through the points to represent the equation y = x − 4 .

Explanation

Understanding the Problem We are given the equation y = x − 4 and a table of x values. Our goal is to complete the table by finding the corresponding y values for each x and then use these points to graph the equation.

Finding the y values For each x value, we substitute it into the equation y = x − 4 to find the corresponding y value.

Calculating y for x = -3 When x = − 3 , y = − 3 − 4 = − 7 .

Calculating y for x = -2 When x = − 2 , y = − 2 − 4 = − 6 .

Calculating y for x = -1 When x = − 1 , y = − 1 − 4 = − 5 .

Calculating y for x = 0 When x = 0 , y = 0 − 4 = − 4 .

Calculating y for x = 1 When x = 1 , y = 1 − 4 = − 3 .

Calculating y for x = 2 When x = 2 , y = 2 − 4 = − 2 .

Calculating y for x = 3 When x = 3 , y = 3 − 4 = − 1 .

Plotting the points and drawing the line Now we have the following points: (-3, -7), (-2, -6), (-1, -5), (0, -4), (1, -3), (2, -2), and (3, -1). We can plot these points on a graph and draw a straight line through them to represent the equation y = x − 4 .

Final Answer The completed table is:





x
y = x - 4



-3
-7


-2
-6


-1
-5


0
-4


1
-3


2
-2


3
-1


The graph of the equation y = x − 4 is a straight line passing through these points.
Examples
Understanding linear equations like y = x − 4 is crucial in many real-world scenarios. For example, imagine you are saving money. If you start with $0 and save $1 each day, but you owe your friend $4 , the equation y = x − 4 models your net savings ( y ) after x days. This equation helps you track when you'll break even and start having positive savings. Linear equations are fundamental in personal finance, physics, and engineering for modeling simple relationships between variables.

Answered by GinnyAnswer | 2025-07-08

To complete the table for the equation y = x − 4 , substitute each x value to find corresponding y values, resulting in the table provided. You can then plot the points derived from the table on a graph and draw a line through them to represent the equation. This exercise helps visualize the linear relationship expressed in the equation.
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Answered by Anonymous | 2025-08-22