What is the x-intercept of the graph of the equation 3x + 3y = -12?
Understand the Problem
The question is asking for the x-intercept of the equation 3x + 3y = -12, which is the point where the graph intersects the x-axis. To find this, we will set y to 0 and solve for x.
Answer
The x-intercept is $(-4, 0)$.
Answer for screen readers
The x-intercept of the equation $3x + 3y = -12$ is $(-4, 0)$.
Steps to Solve
- Set y to zero
To find the x-intercept, we start by setting $y$ to $0$ in the given equation.
$$ 3x + 3(0) = -12 $$
This simplifies to:
$$ 3x = -12 $$
- Solve for x
Next, we solve for $x$. To do this, divide both sides of the equation by $3$:
$$ x = \frac{-12}{3} $$
This gives us:
$$ x = -4 $$
- State the x-intercept
The x-intercept is represented as a point on the graph, which has the coordinates of the form $(x, 0)$. Thus, we can state the final result as:
$$ \text{x-intercept} = (-4, 0) $$
The x-intercept of the equation $3x + 3y = -12$ is $(-4, 0)$.
More Information
The x-intercept is where the graph of a function crosses the x-axis. In this case, when $x = -4$, the value of $y$ is $0$, indicating the specific point where the line intersects the x-axis.
Tips
- Forgetting to set $y$ to $0$ before solving for $x$.
- Miscalculating the division step when simplifying $3x = -12$ to find $x$.
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