Write the linear equation that gives the rule for this table.
X Y
0 77
1 78
2 79
3 80
The linear equation that gives the rule for this table is: Y = X + 77
To find the linear equation that gives the rule for this table, we need to determine the relationship between the values of X and Y.
Looking at the table, we can observe that as X increases by 1, Y also increases by 1. This suggests a linear relationship with a slope of 1.
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. In this case, the slope is 1, so the equation becomes:
Y = 1X + b
Now, let's find the value of b. We can use any of the data points from the table to substitute the values of X and Y into the equation. Let's use the first data point (0, 77):
77 = 1(0) + b
77 = b
Now that we have the value of b, we can substitute it back into the equation:
Y = 1X + 77
Therefore, the linear equation that gives the rule for this table is Y = X + 77.
To find the linear equation that represents the given table, we need to look for the pattern or relationship between the X and Y values.
Let's observe the changes in the X and Y values:
The X value is increasing by 1 each time (0, 1, 2, 3).
The Y value is also increasing by 1 each time (77, 78, 79, 80).
From this observation, we can see that there is a constant rate of change of 1 for both X and Y.
We can use the general form of a linear equation, y = mx + b, where:
- y is the dependent variable (in this case, Y),
- x is the independent variable (in this case, X),
- m represents the slope or rate of change, and
- b represents the y-intercept, where the line crosses the y-axis.
Since the rate of change for both variables is 1, we can substitute m = 1:
y = 1x + b
To find the y-intercept (b), we can choose any point from the table. Let's use the first point (0, 77):
77 = 1(0) + b
77 = b
So the y-intercept (b) is 77.
Now we can substitute the slope (m) and the y-intercept (b) into the equation:
y = 1x + 77
Simplifying the equation, we get:
y = x + 77
Therefore, the linear equation that gives the rule for this table is y = x + 77.