Write the linear equation that gives the rule for this table.
X Y
2 -6
3 -20
4 -34
5 -48
To find the linear equation that gives the rule for this table, we need to look for a pattern in the differences between the values of X and Y. In this case, we can see that as X increases by 1, Y decreases by 14. Therefore, the slope of the linear equation is -14.
Using the point-slope form of a linear equation (y - y1 = m(x - x1)), we can select any point from the table to substitute the values of x1, y1, and m into the equation. Let's use the point (2, -6).
y - (-6) = -14(x - 2)
y + 6 = -14x + 28
y = -14x + 22
So, the linear equation that gives the rule for this table is y = -14x + 22.
To find the linear equation that gives the rule for this table, we need to find the pattern or relationship between the values of x and y.
If we observe the change in y for each increase in x, we can determine that y decreases by -14 when x increases by 1.
To represent this as a linear equation, we can use the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope (m):
Change in y = -14
Change in x = 1
Therefore, the slope (m) is -14.
Next, we need to find the y-intercept (b).
From the table, we can see that when x = 2, y = -6. Substituting these values into the equation, we have:
-6 = -14(2) + b
Simplifying this equation gives us:
-6 = -28 + b
To solve for b, we can add 28 to both sides:
22 = b
So the y-intercept (b) is 22.
Therefore, the linear equation that gives the rule for this table is:
y = -14x + 22
To find the linear equation that gives the rule for this table, we need to determine the relationship between the x-values (X) and the y-values (Y).
By looking at the table, we can observe that when the x-values increase by 1, the y-values decrease by 14. This indicates that the rule is a linear relationship, with a constant rate of change of -14.
To find the equation, we need to determine the y-intercept, which is the value of y when x equals 0. From the table, we can see that when x equals 2, y equals -6.
Now, we can use the general equation of a linear equation, y = mx + b, where m is the slope (rate of change) and b is the y-intercept.
In this case, the slope is -14, and the y-intercept is -6.
Therefore, the linear equation that gives the rule for this table is y = -14x - 6.