We are given the equation of a line $2x - 3y = 6$. Part (a) asks us to find the values of $A$ and $B$ such that the points $(0, A)$ and $(B, 0)$ lie on the line. Part (b) asks us to identify which of the lines C, D, E, or F corresponds to the given equation $2x - 3y = 6$.

1. Problem Description

We are given the equation of a line $2x - 3y = 6$. Part (a) asks us to find the values of $A$ and $B$ such that the points $(0, A)$ and $(B, 0)$ lie on the line. Part (b) asks us to identify which of the lines C, D, E, or F corresponds to the given equation $2x - 3y = 6$.

2. Solution Steps

(a) To find $A$, substitute $x = 0$ into the equation $2x - 3y = 6$:

$2(0) - 3y = 6$

$-3y = 6$

$y = \frac{6}{-3} = -2$

Therefore, $A = -2$.

To find $B$, substitute $y = 0$ into the equation $2x - 3y = 6$:

$2x - 3(0) = 6$

$2x = 6$

$x = \frac{6}{2} = 3$

Therefore, $B = 3$.

(b) The line $2x - 3y = 6$ has intercepts $(0, -2)$ and $(3, 0)$. Examining the graph, we can see that line E passes through $(0, -2)$ and $(3, 0)$.

3. Final Answer

(a) $A = -2$ and $B = 3$

(b) Line E