write the equation for the relationship shown in the graph.

Explanation:

Step1: Identify two - points

Let's take two points on the line. For example, (2, 1) and (20, 18).

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting the points $(x_1,y_1)=(2,1)$ and $(x_2,y_2)=(20,18)$ gives $m=\frac{18 - 1}{20 - 2}=\frac{17}{18}\approx0.944$.

Step3: Use the point - slope form $y - y_1=m(x - x_1)$

Using the point $(2,1)$ and $m = \frac{17}{18}$, we have $y - 1=\frac{17}{18}(x - 2)$.

Step4: Convert to slope - intercept form $y=mx + b$

$y-1=\frac{17}{18}x-\frac{17}{9}$, then $y=\frac{17}{18}x-\frac{17}{9}+1=\frac{17}{18}x-\frac{17 - 9}{9}=\frac{17}{18}x-\frac{8}{9}$.

Answer:

$y=\frac{17}{18}x-\frac{8}{9}$