Question

x | y
5 | 1
12 | 8
16 | 12
18 | 14
y =
(there is also a graph with a purple line, x - axis labeled 0 - 10, y - axis labeled 0 - 10)

Explanation:

Step1: Find slope using two points

Use points $(x_1,y_1)=(5,1)$ and $(x_2,y_2)=(12,8)$.
Slope $m=\frac{y_2-y_1}{x_2-x_1}=\frac{8-1}{12-5}=\frac{7}{7}=1$

Step2: Find y-intercept $b$

Use $y=mx+b$, substitute $m=1$, $x=5$, $y=1$.
$1=1\times5+b$
$b=1-5=-4$

Step3: Write linear equation

Substitute $m=1$ and $b=-4$ into $y=mx+b$.
$y=1\times x -4 = x-4$

Answer:

$y=x-4$