Write the linear equation that gives the rule for this table.
X Y
2 1
3 2
4 3
5 4
The linear equation that gives the rule for this table is: Y = X - 1.
To find the linear equation that gives the rule for this table, we need to determine the relationship between the x-values and y-values. From the table, we can observe that as the x-values increase by 1, the y-values also increase by 1.
The slope of a linear equation represents the rate of change. In this case, the slope is 1, as the y-values increase by 1 for every increase in the x-values by 1.
Using the point-slope form of a linear equation, we can choose any point from the table and substitute the slope to write the equation. Let's choose the point (2, 1):
y - y1 = m(x - x1)
y - 1 = 1(x - 2)
y - 1 = x - 2
y = x - 1
Therefore, the linear equation that gives the rule for this table is y = x - 1.
To find the linear equation that gives the rule for this table, we need to determine the pattern or relationship between the values of X and Y. In this case, it looks like the value of Y is increasing by 1 each time the value of X increases by 1. This suggests that there is a constant rate of change between X and Y.
To express this relationship as a linear equation, we can use the slope-intercept form: Y = mx + b.
First, let's find the slope (m). The slope represents the rate of change between X and Y. To calculate the slope, we can choose any two points from the table and use the formula:
m = (Y2 - Y1) / (X2 - X1)
Let's choose the first two points (2,1) and (3,2):
m = (2 - 1) / (3 - 2)
m = 1 / 1
m = 1
Now that we have the slope (m), we still need to find the y-intercept (b). The y-intercept is the value of Y when X is equal to zero. Since we don't have a point in the table when X is equal to zero, we can calculate the y-intercept by substituting one of the points into the equation:
Using the first point (2,1), we can substitute the values into the equation:
1 = (1)(2) + b
Simplifying the equation:
1 = 2 + b
1 - 2 = b
-1 = b
Now we have the slope (m = 1) and the y-intercept (b = -1).
Putting it all together, the linear equation that gives the rule for this table is:
Y = 1X - 1
or we can simplify it as:
Y = X - 1