A table of values of a linear function is shown below. Find the output when the input is n. Type your answer in the space provided.
input: 1 2 3 4 n
output: -4 -2 0 2 ?
What is the output of n?
To find the output when the input is n, we need to determine the rule or equation that generates the outputs from the inputs. Since the function is linear, we know that it has a constant rate of change or slope.
To find the slope, we can use any two points on the line. Let's use the first and last points:
slope = (output at last input - output at first input) / (last input - first input)
slope = (2 - (-4)) / (4 - 1)
slope = 6/3 = 2
So the slope of the function is 2. Now we can use the point-slope form of the equation of a line to find the output when the input is n:
y - y1 = m(x - x1)
where y is the output, x is the input, m is the slope, and (x1, y1) is any point on the line. Let's use the first point (1, -4):
y - (-4) = 2(x - 1)
y + 4 = 2x - 2
y = 2x - 6
Now we can substitute n for x to find the output when the input is n:
output when input is n = 2n - 6
Therefore, the output when the input is n is 2n - 6.