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

$x = -\frac{3}{2}$

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.

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