What is the x-intercept of the graph of the equation y=2x+6?
Understand the Problem
The question is asking for the x-intercept of the linear equation y=2x+6. To find the x-intercept, we need to set y to 0 and solve for x. This involves finding the value of x when the equation equals zero.
Answer
The x-intercept is $x = -3$.
Answer for screen readers
The x-intercept of the equation $y = 2x + 6$ is $x = -3$.
Steps to Solve
- Set y to 0
To find the x-intercept, we start by substituting $y = 0$ into the equation.
$$ 0 = 2x + 6 $$
- Isolate the variable x
Next, we want to isolate $x$ by moving 6 to the other side of the equation.
$$ 2x = -6 $$
- Solve for x
Now we divide both sides by 2 to find the value of $x$.
$$ x = \frac{-6}{2} $$
- Simplify the solution
This simplifies to:
$$ x = -3 $$
The x-intercept of the equation $y = 2x + 6$ is $x = -3$.
More Information
The x-intercept is the point where the line crosses the x-axis. It is an important concept in graphing linear equations as it helps to understand the position of the line in relation to the axes.
Tips
- A common mistake is to forget to set $y$ to 0 when finding the x-intercept.
- Another mistake is incorrectly simplifying the equation while solving for $x$. To avoid these mistakes, always double-check each step of your calculations.
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