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Finding the intercepts of a linear equation is a crucial first step in graphing. The intercepts help you understand where the line crosses the x-axis and y-axis. Let's break this down further.

Y-Intercept:
To find the y-intercept, set the value of x to zero and solve for y. In our equation, \(3y = -12x\), when \(x = 0\), the equation simplifies to \(3y = 0\). Solving for y, we get \(y = 0\). So, the y-intercept is (0, 0).

X-Intercept:
Similarly, to find the x-intercept, set y to zero and solve for x. For our equation, \(3y = -12x\), when \(y = 0\), the equation simplifies to \(0 = -12x\). Solving for x, we find \(x = 0\). So, the x-intercept is also (0, 0).

Identifying these points ensures accuracy when graphing, and helps you get started on the right foot.

Plotting points on a graph allows you to visualize the linear equation. After finding the intercepts, you should plot them on the graph. For this equation:

• Y-intercept (0, 0)
• X-intercept (0, 0)

Both intercepts are at the origin. To ensure our graph is accurate, we need a third point. Select any x value, for instance:

Choosing a third point:
Let's choose \(x = 1\). Plugging it into the simplified equation \(y = -4x\), we get \(y = -4(1) = -4\). So, our third point is (1, -4).

After plotting these three points, draw a straight line passing through each point. This line represents our equation.

The slope-intercept form of a linear equation is \(y = mx + b\). This form helps to easily identify the slope and y-intercept of the line.

Rewriting our Equation:
Start with the given equation \(3y = -12x\), and divide both sides by 3: \(y = -4x\).

Here, we can identify:

• Slope (m) = -4, which means for every unit increase in x, y decreases by 4 units.
• Y-Intercept (b) = 0, which confirms the y-intercept is (0, 0).

The slope tells us the steepness and direction of the line, while the y-intercept indicates where the line crosses the y-axis. Utilizing the slope-intercept form simplifies graphing and verifying linear equations.