Question

How do I find the y-intercept of a linear equation when it is not provided in a table of values?

Answer 1

To find the y-intercept of a linear equation when it is not given in a table of values, you can follow these steps:

1. **Identify the equation**: If you have the equation written in the slope-intercept form, it will look like \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. The y-intercept is the value of \(y\) when \(x = 0\).

2. **Setting \(x\) to zero**: If you have the equation in a different form (like standard form \(Ax + By = C\) or point-slope form), you can find the y-intercept by setting \(x = 0\) and solving for \(y\).

For example, if you have the equation in standard form \(Ax + By = C\):
- Substitute \(x = 0\): \(A(0) + By = C\), which simplifies to \(By = C\).
- Solve for \(y\): \(y = \frac{C}{B}\). This value is the y-intercept.

3. **Rearranging if necessary**: If your equation is not in a usable form, you may need to rearrange it to find \(y\) in terms of \(x\).

4. **Using a graph (if applicable)**: If you can graph the line represented by the equation, the point where the line crosses the y-axis is the y-intercept.

By applying one of these methods, you can find the y-intercept of a linear equation without needing a table of values.