What is the y-intercept of the graph of the equation 3x + 3y = -12?

Understand the Problem

The question is asking for the y-intercept of the linear equation given. The y-intercept can be found by solving the equation for y when x is set to 0.

Answer

The y-intercept is $b$.
Answer for screen readers

The y-intercept is equal to $b$, which is the constant term in the linear equation.

Steps to Solve

  1. Set x to Zero

To find the y-intercept, we need to substitute $x = 0$ into the given linear equation. This helps us isolate the value of $y$ that corresponds to the point where the line crosses the y-axis.

  1. Substitute and Solve

Substitute $0$ for $x$ in the equation. Suppose the linear equation is in the form $y = mx + b$. Then it becomes:

$$ y = m(0) + b $$

This simplifies to:

$$ y = b $$

  1. Interpret the Result

The value of $b$ is the y-intercept. Therefore, the y-coordinate where the line intersects the y-axis is the value of $b$.

The y-intercept is equal to $b$, which is the constant term in the linear equation.

More Information

The y-intercept represents the value of $y$ when the line crosses the y-axis. In many practical applications, the y-intercept can represent the starting point in problems related to real-world scenarios like finance, physics, and engineering.

Tips

  • Forgetting to set $x$ to zero when calculating the y-intercept.
  • Confusing the slope of the line with the y-intercept.
  • Not simplifying the equation properly.
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