Fill in the missing numbers to complete the linear equation that gives the rule for this table
x y
3 4
4 28
5 52
6 76
no missing numbers
But just keep adding 24. The rule is
y = 24(x-3)+4 = 24x - 68
x y
3 4
4 28
5 52
6 76
===============
76 -52 = 24
52 - 28 = 24
28 - 4 = 24
difference in y for change of 1 in x is 24
so if y = m x + b
then
y = 24 x + b
now when x = 3 y = 4
so
4 = 24 * 3 + b
b = - 68
so
y = 24 x - 68
To find the missing numbers and complete the linear equation, we need to observe the relationship between the given x and y values.
Looking at the table, we can notice that the difference between consecutive y-values is 24. This indicates that the equation is a linear equation with a constant difference.
To find this constant difference, we subtract the y-value of the first row (4) from the y-value of the second row (28): 28 - 4 = 24.
Now that we have the constant difference, we can extend the table.
x y
3 4
4 28
5 52
6 76
The next x-value would be 7, and we can find the corresponding y-value by adding the constant difference to the previous y-value:
76 + 24 = 100
Extending the table further:
x y
3 4
4 28
5 52
6 76
7 100
Now we have a complete table. To find the equation, we can use the point-slope form, which is: y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope.
Let's use the points (3, 4) and (4, 28) to find the equation:
m = (28 - 4) / (4 - 3) = 24 / 1 = 24
(x1, y1) = (3, 4)
Using the point-slope form:
y - 4 = 24(x - 3)
Expanding and simplifying:
y - 4 = 24x - 72
Finally, rearranging the equation to slope-intercept form (y = mx + b):
y = 24x - 72 + 4
y = 24x - 68
Therefore, the rule for the given table is y = 24x - 68.
To find the missing numbers and complete the linear equation for the given table, we need to determine the pattern or rule that relates the values of x and y.
Looking closely at the given table, we notice that the y-values increase by 24 each time the x-value increases by 1. Therefore, the rate of change is constant, and we can conclude that this is a linear relationship.
To find the missing y-values, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, let's calculate the slope (m):
m = (change in y) / (change in x) = (52 - 28) / (5 - 4) = 24 / 1 = 24
Now that we have the slope, we can use any point from the table to find the y-intercept (b). Let's use the point (3, 4):
y = mx + b
4 = (24)(3) + b
4 = 72 + b
To isolate b, we subtract 72 from both sides of the equation:
4 - 72 = b
-68 = b
Now we have the slope (m = 24) and the y-intercept (b = -68). The completed linear equation that gives the rule for the table is:
y = 24x - 68
To find the missing y-values, we can substitute the corresponding x-values into this equation:
For x = 4:
y = 24(4) - 68
y = 96 - 68
y = 28
For x = 6:
y = 24(6) - 68
y = 144 - 68
y = 76
Therefore, the missing y-values to complete the linear equation are 28 and 76.