Let's solve the problem step by step:

Part (a) Find $A$ and $B$:

The line equation is: $3x - 4y = 12$

1. Find $A$: When $x = 0$, the point is $(0, A)$: $3(0) - 4A = 12 \implies -4A = 12 \implies A = -3$ So the coordinate is $(0, -3)$.

2. Find $B$: When $y = 0$, the point is $(B, 0)$: $3B - 4(0) = 12 \implies 3B = 12 \implies B = 4$ So the coordinate is $(4, 0)$.

Thus, $A = -3$ and $B = 4$.

Part (b) Identify the line in the graph:

Using $A = -3$ and $B = 4$, the line passes through $(0, -3)$ and $(4, 0)$.

• We can rewrite the equation into slope-intercept form $y = mx + c$: $3x - 4y = 12 \implies -4y = -3x + 12 \implies y = \frac{3}{4}x - 3$ The slope is $\frac{3}{4}$, and the y-intercept is $-3$.

• Observing the graph:

  • The line with slope $\frac{3}{4}$ and y-intercept $-3$ is labeled Line E.

Final Answer:

1. $A = -3$, $B = 4$
2. The line $3x - 4y = 12$ corresponds to Line E in the graph.

Would you like further clarification?

Here are 5 related questions for practice:

1. Rewrite $3x - 4y = 12$ in standard, slope-intercept, and point-slope forms.
2. Determine the slope of a line perpendicular to $3x - 4y = 12$.
3. Find the equation of the line parallel to $3x - 4y = 12$ passing through $(1, 2)$.
4. How do you find the x- and y-intercepts of any linear equation?
5. Explain the steps to graph $3x - 4y = 12$ without a calculator.

Tip: Remember, you can always confirm intercepts by substituting $x = 0$ or $y = 0$ into the equation!