This exercise is about Linear Functions. From the values given, we can state that:
- The value of missing x = 6
- The value of missing y = 21 (Option D)
What is the explanation for the above?
Given that the table represents a linear function, so the function is a straight line.
Taking two points
(-12, 17)
(-10, 19)
To determine the slope between (-12, 17) and (-10, 19), we need to use the formula:
Slope = (y2-y1)/(x2 - x1)
Recall that:
(x1, y1) = (-12, 17); and
(x2, y2) = (-10, 19)
m = 19 -17/-10 -17
m = 1
Leveraging the point-slope to create the linear equation, we have:
y-y1 = m(x-x1)
where m is the slope of the line and (x₁, y₁) is the point substituting the values m = 1 and the point (-12, 17). Hence, we have:
y-y1 = m(x-x1)
→ y-17 = 1 (x-(-12))
→ y - 17 = x +12
y = x + 12 + 17
y = x + 29 ..................................Linear Equation
Next, we substitute x = -8 into the Linear Equation
y = (-8) + 29
y = 21
Hence, the missing y = 21; and
The missing x = -8
If we substitute y = 23 into the equation, we have:
y = x + 29
23 = x + 29
x = 29 - 23
x = 6
Thus, when the value of y = 23, the missing x is = 6
Conclusively,
The value of missing x = 6
The value of missing y = 21
Full Question
Determine any data values that are missing from the table, assuming that the data represent a linear function.
X Ix ly |-12 17 -10 19 -8 23
a. Missing x:-6 Missing y:22
b. Missing x:-7 Missing y:22
c. Missing x:-7 Missing y:20
d. Missing x:-6 Missing y:21
Please select the best answer from the choices provided.
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