which is the graph of the equation $y - 1=\frac{2}{3}(x - 3)$?

Explanation:

Step1: Rewrite in slope - intercept form

Starting with $y - 1=\frac{2}{3}(x - 3)$, distribute the $\frac{2}{3}$: $y-1=\frac{2}{3}x-2$. Then add 1 to both sides to get $y=\frac{2}{3}x - 1$.

Step2: Identify slope and y - intercept

The slope $m=\frac{2}{3}$ and the y - intercept $b=-1$.

Step3: Check points on the line

For the point - slope form $y - 1=\frac{2}{3}(x - 3)$, when $x = 3$, $y-1=\frac{2}{3}(3 - 3)=0$, so $y = 1$. When $x=0$, $y-1=\frac{2}{3}(0 - 3)=- 2$, so $y=-1$.

We can check the given graphs for a line with slope $\frac{2}{3}$ and passing through points like $(3,1)$ and $(0,-1)$.

Answer:

(There is no option text provided to choose from, but the correct graph is a straight - line with slope $\frac{2}{3}$ and y - intercept at $(0,-1)$ and passing through $(3,1)$)