What is the y-intercept of the graph of the equation y = 2x + y = 3?
Understand the Problem
The question is asking for the y-intercept of the given equation. To find the y-intercept, we need to rewrite the equation in standard form and set x to zero, solving for y.
Answer
The y-intercept is $y = \frac{c}{b}$.
Answer for screen readers
The y-intercept is $y = \frac{c}{b}$.
Steps to Solve
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Identify the equation
First, write down the given equation. For example, let’s say the equation is in this form: $$ ax + by = c $$ -
Set x to zero
To find the y-intercept, set $x = 0$ in the equation. This allows us to find the value of $y$ when the line crosses the y-axis. For example: $$ a(0) + by = c $$ -
Simplify the equation
This simplifies to: $$ by = c $$ -
Solve for y
Now, divide by $b$ to isolate $y$: $$ y = \frac{c}{b} $$ -
Identify the y-intercept
The value obtained from the above equation gives us the y-intercept, which is the point $(0, \frac{c}{b})$ on the graph.
The y-intercept is $y = \frac{c}{b}$.
More Information
The y-intercept is the point where a line crosses the y-axis, and it occurs when $x = 0$. It's useful in graphing linear equations and understanding their behavior.
Tips
- Forgetting to set $x$ to zero before solving for $y$.
- Miscalculating the value of $c$ and $b$, leading to the wrong y-intercept. Always double-check your arithmetic.
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