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Explain Bot To find the equation that generates the values in the table, you need to observe the pattern or relationship between the x-values and the corresponding y-values. Let's analyze the data:
When the x-value is -3, the y-value is 1.
When the x-value is -1, the y-value is 3.
When the x-value is 0, the y-value is 5.
When the x-value is 1, the y-value is 7.
When the x-value is 2, the y-value is 9.
To determine the equation, we can note that the y-values increase by 2 each time the x-value increases by 1. This suggests a linear relationship.
To confirm this, we can calculate the difference between successive y-values:
3 - 1 = 2
5 - 3 = 2
7 - 5 = 2
9 - 7 = 2
The difference between the y-values is constant, indicating a linear relationship.
Now let's use the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept. We can calculate the slope by selecting any two points from the table:
Using the points (0, 5) and (-1, 3):
m = (y2 - y1) / (x2 - x1)
= (3 - 5) / (-1 - 0)
= -2 / -1
= 2
Now that we have the slope, we can plug it into the equation in the form y = mx + b, along with any of the given coordinates:
Using the point (0, 5):
5 = 2(0) + b
5 = 0 + b
b = 5
Finally, we have the slope (m = 2) and the y-intercept (b = 5), allowing us to write the equation that generates the values in the table:
y = 2x + 5
Therefore, the equation that generates the values in the table is y = 2x + 5.