Write the linear equation that gives the rule for this table.
X Y
2 -60
3 -67
4 -74
5 -81
The linear equation that gives the rule for this table can be represented as:
y = -7x - 46
To find the linear equation that gives the rule for this table, we need to determine the relationship between the x-values and the y-values.
From the given table, we can see that the y-values are decreasing by 7 each time the x-value increases by 1.
Let's denote the x-value by "x" and the y-value by "y".
Since the y-values are decreasing by 7 each time the x-value increases by 1, we can write the equation as:
y = mx + b
where "m" is the slope and "b" is the y-intercept.
To determine the slope, we can take any two points from the table. Let's choose the points (2, -60) and (3, -67).
m = (change in y) / (change in x)
= (-67 - (-60)) / (3 - 2)
= (-67 + 60) / (3 - 2)
= -7 / 1
= -7
Now, let's substitute the slope "m" and one point "(2, -60)" into the equation:
-60 = (-7)(2) + b
Simplifying this equation, we get:
-60 = -14 + b
To find the value of "b", we can add 14 to both sides:
-60 + 14 = b
b = -46
Therefore, the linear equation that gives the rule for this table is:
y = -7x - 46
To write a linear equation that gives the rule for the given table, we need to determine the relationship between the x-values and the y-values. When we look at the y-values, we can see that they are decreasing by 7 as the x-values increase by 1. This suggests that the linear equation has a slope of -7.
To find the y-intercept, which is the value of y when x is 0, we can substitute any x and y pair from the table into the linear equation and solve for the y-intercept.
Let's use the first row of the table (x=2, y=-60) to find the y-intercept:
y = mx + b
-60 = -7(2) + b
-60 = -14 + b
b = -60 + 14
b = -46
Now that we have the slope (m = -7) and the y-intercept (b = -46), we can write the linear equation in slope-intercept form:
y = -7x - 46
Therefore, the linear equation that gives the rule for the given table is y = -7x - 46.