Complete The Table For The Equation $y = 2x$.$\[ \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline $x$ & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline $y$ & & & & & & & &
Solving the Equation
The equation is a linear equation in the slope-intercept form, where the slope is 2 and the y-intercept is 0. This equation represents a straight line that passes through the origin (0, 0) and has a slope of 2. In this article, we will complete the table for the equation by finding the corresponding values of y for different values of x.
Understanding the Equation
The equation can be rewritten as , where 0 is the y-intercept. This means that for every value of x, the corresponding value of y is twice the value of x. For example, if x is 2, then y is 2(2) = 4.
To complete the table, we need to find the corresponding values of y for different values of x. We can do this by substituting the values of x into the equation and solving for y.
| x | y |
|---|---|
| -3 | |
| -2 | |
| -1 | |
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 |
Finding the Values of y
To find the values of y, we can substitute the values of x into the equation and solve for y.
- For x = -3, we have y = 2(-3) = -6.
- For x = -2, we have y = 2(-2) = -4.
- For x = -1, we have y = 2(-1) = -2.
- For x = 0, we have y = 2(0) = 0.
- For x = 1, we have y = 2(1) = 2.
- For x = 2, we have y = 2(2) = 4.
- For x = 3, we have y = 2(3) = 6.
- For x = 4, we have y = 2(4) = 8.
Completed Table
| x | y |
|---|---|
| -3 | -6 |
| -2 | -4 |
| -1 | -2 |
| 0 | 0 |
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |
The equation represents a straight line that passes through the origin (0, 0) and has a slope of 2. The completed table shows the corresponding values of y for different values of x. We can see that for every value of x, the corresponding value of y is twice the value of x.
In this article, we completed the table for the equation by finding the corresponding values of y for different values of x. We can use this table to visualize the graph of the equation and understand its behavior. The equation is a simple linear equation, but it has many real-world applications, such as modeling the growth of populations, the cost of goods, and the distance traveled by an object.
Real-World Applications
The equation has many real-world applications, such as:
- Modeling the growth of populations: The equation can be used to model the growth of populations, where y is the population size and x is the time.
- Modeling the cost of goods: The equation can be used to model the cost of goods, where y is the cost and x is the quantity.
- Modeling the distance traveled by an object: The equation can be used to model the distance traveled by an object, where y is the distance and x is the time.
In conclusion, the equation is a simple linear equation that has many real-world applications. By completing the table for the equation, we can visualize the graph of the equation and understand its behavior. The equation is a fundamental concept in mathematics and has many practical applications in various fields.