Write the linear equation that gives the rule for this table.
X Y
0 -20
1 -39
2 -58
3 -77
The linear equation that gives the rule for this table is:
Y = -19X - 20
To find the linear equation for this table, we will look for a pattern in the relationship between the X and Y values.
Looking at the difference between the X values, we can see that each X value increases by 1 each time. Therefore, the relationship between the X values is linear.
Now let's focus on the relationship between the X and Y values. Looking at the difference between the Y values, we can observe that each Y value decreases by 19 each time the X value increases by 1. Therefore, the relationship between the X and Y values is also linear.
To find the equation, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
To find the slope (m), we can use the difference in the Y values divided by the difference in the X values. Let's take the first two data points as an example:
(X1, Y1) = (0, -20)
(X2, Y2) = (1, -39)
The difference in the X values is 1 - 0 = 1.
The difference in the Y values is -39 - (-20) = -19.
Therefore, the slope (m) is -19 / 1 = -19.
Now that we know the slope, we can find the y-intercept (b) by substituting the values of one of the points into the equation.
Let's use the first point (X1, Y1):
0 = -19(0) + b
Simplifying further, we get b = -20.
Hence, the linear equation that gives the rule for this table is:
y = -19x - 20
To find the linear equation that gives the rule for this table, we need to determine the pattern or relationship between the values of X and Y. In a linear equation, the relationship between X and Y can be described by the formula:
Y = mX + b
Where m is the slope of the line and b is the y-intercept.
To find the slope (m), we can use any two points from the table. Let's choose the points (0, -20) and (1, -39).
m = (Y2 - Y1) / (X2 - X1)
= (-39 - (-20)) / (1 - 0)
= -19 / 1
= -19
Now, let's substitute the value of the slope into the equation:
Y = -19X + b
Next, we need to find the y-intercept (b). We can use any point on the line. Let's choose the point (0, -20).
-20 = -19(0) + b
-20 = b
Finally, we can substitute the value of b into the equation:
Y = -19X - 20
Therefore, the linear equation that gives the rule for this table is Y = -19X - 20.