Question

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 5 9 13 17
(there are also some operation buttons like +, -, ×, ÷ and undo, close buttons)

Explanation:

Step1: Find the slope (rate of change)

The slope $m$ is calculated as $\frac{\text{Change in output}}{\text{Change in input}}$. Using input 1 (output 5) and input 2 (output 9):
$m = \frac{9-5}{2-1} = 4$

Step2: Find the y-intercept ($b$)

Use the linear function form $y = mx + b$, substitute $x=1$, $y=5$, $m=4$:
$5 = 4(1) + b$
Solve for $b$: $b = 5 - 4 = 1$

Step3: Write the linear function

Substitute $m=4$ and $b=1$ into $y = mx + b$, where input is $n$ and output is $y$:
$y = 4n + 1$

Answer:

$4n + 1$