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
- 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.
- 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:
$$ y = b $$
- 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.
