Question

graph -12x - 3y = 6.

Explanation:

Step1: Convert to slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We start with the equation $- 12x-3y = 6$. First, we want to solve for $y$.
Add $12x$ to both sides of the equation: $-3y=12x + 6$.
Then, divide each term by $- 3$: $y=\frac{12x}{-3}+\frac{6}{-3}$, which simplifies to $y=-4x - 2$.

Step2: Identify the slope and y - intercept

From the equation $y=-4x - 2$, the slope $m=-4$ and the y - intercept $b = - 2$. The y - intercept is the point where the line crosses the y - axis, so the point is $(0,-2)$.

Step3: Find another point using the slope

The slope $m=\frac{\text{rise}}{\text{run}}=-4=\frac{-4}{1}$. Starting from the point $(0,-2)$, we move down 4 units (because the rise is - 4) and 1 unit to the right (because the run is 1). This gives us the point $(0 + 1,-2-4)=(1,-6)$.

Step4: Plot the points and draw the line

Plot the points $(0,-2)$ and $(1,-6)$ on the coordinate plane. Then, draw a straight line passing through these two points. This line represents the graph of the equation $-12x - 3y=6$.

Answer:

The graph of the line $y = - 4x-2$ (which is equivalent to $-12x - 3y = 6$) has a y - intercept at $(0,-2)$ and a slope of $-4$. It can be graphed by plotting the points $(0,-2)$ and $(1,-6)$ (and other points found using the slope) and drawing a straight line through them.