To determine which equation matches the provided data from the table, let’s break it down step by step. The table consists of various relationships between the variables y and x. The given statements are:
- y = x
- y = 3
- y = 4x
- y = x + 3
To analyze these equations:
1. y = x
This equation represents a linear relationship where y equals x. The graph of this equation is a straight line that passes through the origin at a 45-degree angle.
2. y = 3
This equation indicates that y is a constant value of 3, regardless of x. The graph is a horizontal line intersecting the y-axis at 3.
3. y = 4x
This equation implies that y is four times the value of x. It is another linear relationship, but with a steeper slope, as every increase in x results in a larger increase in y.
4. y = x + 3
This equation shows that y increases linearly with x, but it is shifted upwards by 3 units on the y-axis. The slope is 1, similar to y = x, but with a different y-intercept.
To determine which equation matches the table requires knowing the specific values given for y and x. Depending on the values in the table, you will select the corresponding equation. For example:
- If x = 1, then for y = x, y would be 1.
- For y = 3, no matter what x is, y remains 3.
- If x = 1, then for y = 4x, y would be 4.
- If x = 1, then y = x + 3 would result in y being 4.
So, if the table contains a row where y = 3, y = 4, etc., you can check each equation to see which one aligns with the values from the table. Therefore, knowing the specific x and y values in the table is essential to match with any of the listed equations correctly.