Write the linear equation that gives the rule for this table.
X Y
4 0
5 1
6 2
7 3
The linear equation that gives the rule for this table is y = x - 4.
To find the linear equation that represents the rule for this table, we need to determine the relationship between the values of X and Y.
From the table, we can see that as X increases by 1, Y also increases by 1. This suggests that the relationship between X and Y is linear.
Using the information from the table, we can find the slope of the line. The slope of a linear equation is equal to the change in Y divided by the change in X.
Change in Y = 2 - 0 = 2
Change in X = 6 - 4 = 2
Slope = Change in Y / Change in X = 2 / 2 = 1
Now, let's use the slope-intercept form of a linear equation, which is:
Y = mx + b
where m represents the slope and b represents the y-intercept.
We already know the slope (m = 1), so we just need to find the y-intercept.
To find the y-intercept, we can use any point from the table. Let's choose the point (4, 0).
Y = mx + b
0 = 1 * 4 + b
Now, we can solve for b:
0 = 4 + b
b = 0 - 4
b = -4
Therefore, the linear equation that gives the rule for this table is:
Y = X - 4
To write the linear equation that gives the rule for this table, we need to identify a pattern and then use that pattern to determine the equation.
Looking at the table, we can see that as the value of X increases by 1, the value of Y increases by 1 as well. This indicates a constant rate of change, which suggests a linear relationship between X and Y.
To find the equation, we can use the slope-intercept form, which is given by y = mx + b, where m is the slope and b is the y-intercept.
To find the slope (m), we can take any two points in the table and calculate the change in Y divided by the change in X. Let's use the points (4, 0) and (5, 1):
m = (1 - 0) / (5 - 4)
m = 1 / 1
m = 1
So, the slope is 1.
To find the y-intercept (b), we can substitute the values of one of the points into the equation and solve for b. Let's use the point (4, 0):
0 = 1 * 4 + b
0 = 4 + b
b = -4
Therefore, the y-intercept is -4.
Now that we have the slope and y-intercept, we can write the linear equation:
y = 1x - 4
Simplifying, we get:
y = x - 4
Therefore, the linear equation that gives the rule for this table is y = x - 4.