Write an equation for a function that gives the values in each table, and then find the missing terms.
X: -1, 0, 1, 2, 5, 7
Y: ?, 3.4, 4.4, 5.4, ?, 10.4
To find the equation for the given function, we need to determine the pattern between the values of X and Y in the table. Then we can use that pattern to find the missing terms in the table.
Looking at the X values, we can observe that there is a constant difference of 1 between each consecutive term: -1, 0, 1, 2, 5, 7. This suggests that X follows a linear pattern.
Now let's examine the Y values. From the table, we see that the Y values increase by a constant difference of 1 from one term to the next: 3.4, 4.4, 5.4, 6.4. This indicates that Y also follows a linear pattern.
To find the equation for the function, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
We can start by finding the slope (m). We choose two points (-1, ?) and (0, 3.4) from the table. Using the slope formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) = (-1, ?) and (x2, y2) = (0, 3.4).
m = (3.4 - ?) / (0 - (-1))
= (3.4 - ?) / (1)
= 3.4 - ?
Next, we can substitute one of the points (either (-1, ?) or (0, 3.4)) into the slope-intercept form equation y = mx + b to find the value of b (the y-intercept).
Using the point (0, 3.4):
3.4 = (3.4 - ?)(0) + b
3.4 = b
Now we have the value of b, which is 3.4. So the equation for the function is y = 3.4x + 3.4.
Now we can use this equation to find the missing terms in the table.
Substituting x = 5 into the equation:
y = 3.4(5) + 3.4
= 17 + 3.4
= 20.4
So the missing term in the table where x = 5 is 20.4.
Similarly, substituting x = 7 into the equation:
y = 3.4(7) + 3.4
= 23.8 + 3.4
= 27.2
Thus, the missing term in the table where x = 7 is 27.2.
The complete table is:
X: -1, 0, 1, 2, 5, 7
Y: 3.4, 4.4, 5.4, 6.4, 20.4, 27.2
Therefore, the equation for the function is y = 3.4x + 3.4, and the missing terms in the table are 20.4 and 27.2.