A table of values of a linear function is shown below. Find the output when the input is n.
Input: 1 2 3 4 n
Output: 0 2 4 6 ?
To find the output when the input is n, we first need to identify the pattern in the table of values.
From the given table, we can see that the output (y) increases by 2 each time the input (x) increases by 1. This indicates that the function is linear, with a slope of 2.
To find the output when the input is n, we can use the formula for a linear function: y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope (m) is 2, as the output increases by 2 for each increase in the input by 1.
Now we need to find the y-intercept (b) in order to write the equation of the linear function.
From the table of values, we can see that when the input is 1, the output is 0. This means that the y-intercept is 0.
Therefore, the equation of the linear function is: y = 2x
Now we can find the output when the input is n by substituting n for x in the equation:
y = 2n
So, the output when the input is n is 2n.
How do you find the slope of a line?
To find the slope of a line, you can use the following formula:
slope = (change in y) / (change in x) = (y2 - y1) / (x2 - x1)
This formula is also known as the "rise over run" formula, where the change in y represents how much the line moves up or down and the change in x represents how much the line moves left or right.
To find the slope of a line, you need to choose two points on the line (x1, y1) and (x2, y2). Then, substitute the coordinates of these two points into the formula to calculate the slope.
For example, given the points (2, 4) and (5, 10), you can find the slope of the line passing through these two points by using the formula:
slope = (10 - 4) / (5 - 2) = 6 / 3 = 2
Therefore, the slope of the line passing through the points (2, 4) and (5, 10) is 2.