What is the x-intercept of the graph of the equation y = 2x + y = 3?
Understand the Problem
The question is asking for the x-intercept of the equation y = 2x + y = 3. To find the x-intercept, we need to set y to 0 and solve for x.
Answer
$x = -\frac{3}{2}$
Answer for screen readers
The x-intercept is $x = -\frac{3}{2}$.
Steps to Solve
- Set y to 0
To find the x-intercept, we set $y = 0$ in the equation $y = 2x + 3$.
- Substitute y in the equation
Now we substitute $y$ with $0$: $$ 0 = 2x + 3 $$
- Isolate x
Next, we solve for $x$ by isolating it on one side of the equation: $$ 2x = -3 $$
- Divide by 2
Finally, divide both sides by $2$ to find the value of $x$: $$ x = -\frac{3}{2} $$
The x-intercept is $x = -\frac{3}{2}$.
More Information
The x-intercept is where the line crosses the x-axis, and in this case, it indicates that when $y$ is 0, the value of $x$ is $-\frac{3}{2}$. This means that the point $(-\frac{3}{2}, 0)$ is where the graph intersects the x-axis.
Tips
- A common mistake is to forget to set $y$ to $0$ before solving for $x$.
- Another mistake can be miscalculating when isolating $x$, so it's important to double-check arithmetic.