Question

x | y
3 | 11
5 | 13
8 | 16
10 | 18
y =

Explanation:

Step1: Identify linear relationship form

We use the linear equation $y = mx + b$, where $m$ is slope, $b$ is y-intercept.

Step2: Calculate slope $m$

Use two points $(x_1,y_1)=(3,11)$ and $(x_2,y_2)=(5,13)$:
$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{13-11}{5-3} = \frac{2}{2} = 1$$

Step3: Find y-intercept $b$

Substitute $m=1$, $x=3$, $y=11$ into $y=mx+b$:
$$11 = 1\times3 + b$$
$$b = 11 - 3 = 8$$

Step4: Verify with other points

For $x=8$: $y=1\times8 +8=16$, which matches. For $x=10$: $y=1\times10 +8=18$, which matches.

Answer:

$y = x + 8$