I am really confused!!!
how do you make a table for solutions? For example y=2x The table of solutions shows 0,0; 1,2; -1,-2;2,4;-2,-4 The would than be plotted on a graph. What I can't figure out is how they got the pairs.
You plug in one value as 'x' to find 'y'. or vice versa.
ex. y=2x
I will use 1 for x
2*1=2 so, y=2
WHen you plot this on a graph you plot it as (1,2). 1 being on the x-axis, and 2 on the y-axis.
To create a table of solutions for a given equation, such as y = 2x, you can follow these steps:
Step 1: Choose some values for x.
You can start by selecting a few different values for x. These values will help you find the corresponding y-values.
Step 2: Substitute the chosen x-values into the equation to find the corresponding y-values.
For each chosen x-value, substitute it into the equation y = 2x, and solve for y. This will give you the corresponding y-values.
Step 3: Create a pair of x and y values for each corresponding solution.
Write down the pairs of x and y values you obtained from substituting the x-values into the equation. These pairs represent the solutions.
For example, let's create a table of solutions for the equation y = 2x using the chosen values of x: 0, 1, -1, 2, and -2.
Step 1: Choose values for x:
x = 0, 1, -1, 2, -2
Step 2: Substitute x into the equation to find y:
For x = 0:
y = 2(0) = 0
So, the first pair is (0, 0).
For x = 1:
y = 2(1) = 2
The second pair is (1, 2).
For x = -1:
y = 2(-1) = -2
The third pair is (-1, -2).
For x = 2:
y = 2(2) = 4
The fourth pair is (2, 4).
For x = -2:
y = 2(-2) = -4
The fifth pair is (-2, -4).
Step 3: Create a table of solutions:
x | y
-----------
0 | 0
1 | 2
-1 | -2
2 | 4
-2 | -4
These pairs of x and y values represent the solutions of the given equation. Now, you can plot these points on a graph to visualize the relationship between x and y.
I understand your confusion. To create a table of solutions for an equation like y=2x, you need to substitute different values for x and then calculate the corresponding values of y. Let me show you step-by-step how to generate the pairs of values:
Step 1: Choose a range of x-values: It's usually helpful to start with a few simple and easy-to-work-with values. In this case, let's select -2, -1, 0, 1, and 2 as the x-values.
Step 2: Substitute the x-values into the equation: For each chosen x-value, substitute it into the equation y=2x and calculate the corresponding y-value. Let's go through each x-value one by one:
- For x = -2: Substitute x = -2 into the equation, y = 2(-2), which equals y = -4. So the first pair is (-2, -4).
- For x = -1: Substitute x = -1 into the equation, y = 2(-1), which equals y = -2. The second pair is (-1, -2).
- For x = 0: Substitute x = 0 into the equation, y = 2(0), which equals y = 0. The third pair is (0, 0).
- For x = 1: Substitute x = 1 into the equation, y = 2(1), which equals y = 2. The fourth pair is (1, 2).
- For x = 2: Substitute x = 2 into the equation, y = 2(2), which equals y = 4. The fifth pair is (2, 4).
Now, you have all the pairs of values for x and y: (-2, -4), (-1, -2), (0, 0), (1, 2), and (2, 4).
Finally, you can plot these pairs on a graph, where the x-values are plotted on the x-axis and the y-values are plotted on the y-axis. Connecting these points will result in a straight line graph representing the equation y=2x.
I hope this helps! Let me know if you have any further questions or if there's anything else I can assist you with.