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


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

Calculate y values for given x values using y = − 4 x .
Create a table with x and corresponding y values.
Plot the points from the table on a graph.
Draw a straight line through the points to represent the equation y = − 4 x .
The final graph represents the linear equation y = − 4 x .

Explanation

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

Calculating y values Let's calculate the y values for each x value using the equation y = − 4 x :


For x = − 3 , we have y = − 4 ( − 3 ) = 12 .
For x = − 2 , we have y = − 4 ( − 2 ) = 8 .
For x = − 1 , we have y = − 4 ( − 1 ) = 4 .
For x = 0 , we have y = − 4 ( 0 ) = 0 .
For x = 1 , we have y = − 4 ( 1 ) = − 4 .
For x = 2 , we have y = − 4 ( 2 ) = − 8 .
For x = 3 , we have y = − 4 ( 3 ) = − 12 .

Table of Values and Points Now we have the following table of values:




x
y = -4x



-3
12


-2
8


-1
4


0
0


1
-4


2
-8


3
-12


These points can be plotted on a graph. The points are (-3, 12), (-2, 8), (-1, 4), (0, 0), (1, -4), (2, -8), and (3, -12).

Graphing the Equation Plotting these points on a graph and drawing a straight line through them will give us the graph of the equation y = − 4 x .

Final Answer The graph of the equation y = − 4 x is a straight line passing through the origin (0, 0). The slope of the line is -4, which means that for every increase of 1 in the x value, the y value decreases by 4.


Examples
Understanding linear equations like y = − 4 x is crucial in many real-world scenarios. For instance, imagine you're tracking the depreciation of a car's value over time. If the car loses 4 , 000 in v a l u ee a c h ye a r , yo u c an re p rese n tt hi sre l a t i o n s hi pw i t h t h ee q u a t i o n y = -4x , w h ere y i s t h e t o t a l d e p rec ia t i o nan d x$ is the number of years. By plotting this equation, you can easily visualize how the car's value decreases over time and predict its value in the future. This concept extends to various fields, including finance, physics, and engineering, where linear relationships are used to model and predict outcomes.

Answered by GinnyAnswer | 2025-07-08