Write the linear equation that gives the rule for this table.
X Y
1 -37
2 -32
3 -27
4 -22
The linear equation that gives the rule for this table is y = -5x - 42.
To find the linear equation that represents the relationship between X and Y in the given table, we can look for a pattern in the Y values.
From the table, we can see that as X increases by 1, Y increases by 5. This suggests that the slope of the equation is 5.
To find the y-intercept, we can plug in the values of X = 1 and Y = -37 into the equation and solve for the y-intercept:
Y = mx + b
-37 = 5(1) + b
-37 = 5 + b
b = -37 - 5
b = -42
Putting the slope, m = 5, and the y-intercept, b = -42, into the equation, we get:
Y = 5X - 42.
Therefore, the linear equation that gives the rule for this table is Y = 5X - 42.
To find the linear equation that gives the rule for this table, you need to determine the relationship between the x-values and the y-values.
Let's analyze the given table:
X Y
1 -37
2 -32
3 -27
4 -22
The x-values increase by 1 each time, while the y-values increase by 5 each time. This indicates that there is a constant rate of change between the x and y values. In this case, the rate of change is +5.
To determine the y-intercept, we can observe that when x = 0 (which is not given in the table), y would be -42 (the y-value decreases by 5 for each increase in x). Therefore, the y-intercept is -42.
Now that we know the rate of change (5) and the y-intercept (-42), we can write the linear equation in the form of y = mx + b, where m represents the slope (rate of change) and b represents the y-intercept.
Therefore, the linear equation that gives the rule for this table is:
y = 5x - 42