Write the linear equation that gives the rule for this table.
X Y
0 63
1 24
2 -15
3 -54
The linear equation for this table can be represented as:
Y = -39X + 63
To find the linear equation that gives the rule for this table, we need to identify the relationship between the x-values and y-values.
Looking at the table, we can observe that the y-values decrease by 39 as the x-values increase by 1. This means that there is a constant rate of change of -39 between the x-values and y-values.
Since the y-intercept is the value of y when x is 0, we can see that when x is 0, y is 63. Therefore, the y-intercept is 63.
Using this information, we can write the linear equation in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
The slope (m) is the constant rate of change, which is -39. The y-intercept (b) is 63.
Thus, the equation that gives the rule for this table is:
y = -39x + 63
To write the linear equation that gives the rule for this table, we need to find the relationship between the X and Y values.
Let's examine the difference between consecutive X values and the difference between consecutive Y values.
For the X values:
1 - 0 = 1
2 - 1 = 1
3 - 2 = 1
The difference between consecutive X values is constant, which indicates a linear relationship.
Similarly, for the Y values:
24 - 63 = -39
-15 - 24 = -39
-54 - (-15) = -39
The difference between consecutive Y values is also constant, indicating a linear relationship.
Now, let's find the equation for this linear relationship.
We can start by finding the slope (m) by dividing the difference in Y values by the difference in X values:
m = (Y2 - Y1) / (X2 - X1)
= (-15 - 24) / (2 - 1)
= -39 / 1
= -39
Now, let's use the slope (m) and one point from the table (0, 63) to find the equation using the point-slope form:
y - y1 = m(x - x1)
Substituting the values:
y - 63 = -39(x - 0)
Expanding the equation:
y - 63 = -39x + 0
Simplifying the equation:
y = -39x + 63
Therefore, the linear equation that gives the rule for this table is y = -39x + 63.