Write the linear equation that gives the rule for this table.
X Y
0 55
1 30
2 5
3 -20
To find the linear equation that gives the rule for this table, we need to identify the slope and y-intercept.
We can find the slope (m) by using the formula:
m = (change in y) / (change in x)
Using the given table, we can calculate the change in y and change in x:
Change in y = 30 - 55 = -25
Change in x = 1 - 0 = 1
So the slope (m) is -25/1 = -25.
Next, we need to find the y-intercept (b). We can choose any point from the table to plug into the equation y = mx + b and solve for b. Let's use the point (0, 55):
55 = -25(0) + b
55 = b
Therefore, the y-intercept (b) is 55.
Now we have the slope (m = -25) and y-intercept (b = 55), so we can write the linear equation:
y = -25x + 55
To find the equation that represents the relationship between X and Y in the given table, we can use the general form of a linear equation, which is y = mx + b.
Step 1: Find the slope (m) of the line.
To find the slope, we can take any two points from the table and use the formula: m = (y2 - y1) / (x2 - x1).
Let's take the points (0, 55) and (1, 30).
m = (30 - 55) / (1 - 0)
m = -25
Step 2: Find the y-intercept (b) of the line.
To find the y-intercept, we can substitute the slope (m) and any point from the table (x, y) into the equation y = mx + b and solve for b.
Let's use the point (0, 55).
55 = -25 * 0 + b
55 = b
Step 3: Write the equation.
Now that we have the slope (m) and the y-intercept (b), we can write the equation.
y = -25x + 55
Therefore, the linear equation that gives the rule for this table is y = -25x + 55.
To write the linear equation that represents the rule for the given table, we need to determine the relationship between the variables X and Y.
From the table, we can observe that as X increases by 1, Y decreases by 25. This suggests that there is a constant rate of change between X and Y.
Let's calculate the difference in Y-values as X increases by 1:
Y2 - Y1 = 30 - 55 = -25
Y3 - Y2 = 5 - 30 = -25
Y4 - Y3 = -20 - 5 = -25
We can see that the difference in Y-values is consistent (-25) as X increases by 1. Therefore, we can conclude that the slope of the linear equation is -25.
Now, let's find the y-intercept. We can choose any point from the table to substitute into the slope-intercept form of a linear equation: y = mx + b.
Considering the point (0, 55), we have:
55 = -25(0) + b
55 = b
Since the y-intercept (b) is 55, the equation can be written as:
y = -25x + 55
Thus, the linear equation that gives the rule for this table is y = -25x + 55.