The problem asks us to find the x-intercept and y-intercept of the equation $-4x - 3y = 6$, and then graph the equation.

1. Problem Description

The problem asks us to find the x-intercept and y-intercept of the equation $-4x - 3y = 6$, and then graph the equation.

2. Solution Steps

To find the x-intercept, we set $y = 0$ and solve for $x$:

$-4x - 3(0) = 6$

$-4x = 6$

$x = -\frac{6}{4} = -\frac{3}{2}$

So, the x-intercept is $(-\frac{3}{2}, 0)$.

To find the y-intercept, we set $x = 0$ and solve for $y$:

$-4(0) - 3y = 6$

$-3y = 6$

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

So, the y-intercept is $(0, -2)$.

We can also find another point on the line to check our work. Let's set $x = 3$:

$-4(3) - 3y = 6$

$-12 - 3y = 6$

$-3y = 18$

$y = -6$

So, the point $(3, -6)$ is on the line.

3. Final Answer

x-intercept: $(-\frac{3}{2}, 0)$

y-intercept: $(0, -2)$