Write the linear equation that gives the rule for this table.
X Y
2 -38
3 -57
4 -76
5 -95
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 see that for each X value, Y decreases by 19.
Therefore, we can say that the change in Y (ΔY) is -19 times the change in X (ΔX) for each pair of consecutive values.
From the given table, we can write the second difference for Y:
(ΔY₁) = -19
Now we can write the general form of the equation in slope-intercept form (y = mx + b), replacing m with ΔY₁ and b with the y-coordinate of a point on the line.
Using the point (2, -38), we can substitute X = 2 and Y = -38 into the equation to find b:
-38 = -19(2) + b
-38 = -38 + b
b = 0
Thus, the equation that gives the rule for this table is:
Y = -19X
To find the linear equation for this table, we need to determine the pattern between the x-values (X) and the corresponding y-values (Y). Notice that the y-values decrease by 19 each time the x-value increases by 1. This suggests that the slope of the linear equation is -19.
We can also observe that when x = 2, y = -38. This indicates that the y-intercept is -38.
Therefore, the linear equation that gives the rule for this table is:
Y = -19X - 38
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 the value of X increases by 1, the value of Y decreases by 19. This indicates that there is a constant rate of change of -19 between X and Y.
To find the equation, we can use the slope-intercept form of a linear equation, which is given by:
Y = mX + b
Where:
- Y represents the dependent variable (in this case, the value of Y)
- X represents the independent variable (in this case, the value of X)
- m represents the slope of the line
- b represents the y-intercept (the value of Y when X is 0)
Since we know that the slope (m) is -19, we just need to find the y-intercept (b).
To find the y-intercept, we can substitute one pair of X and Y values from the table into the equation and solve for b. Let's use the first pair, which is (2, -38).
-38 = -19(2) + b
-38 = -38 + b
b = -38 + 38
b = 0
Now that we have both the slope (m = -19) and the y-intercept (b = 0), we can write the linear equation:
Y = -19X + 0
Since the term + 0 doesn't affect the equation, we can simplify it to:
Y = -19X
Therefore, the linear equation that gives the rule for this table is Y = -19X.