# How to find the y-intercept from two points?

#### Understand the Problem

The question is asking how to derive the y-intercept of a linear equation based on two given points. To solve this, we typically find the slope using the two points and then use the slope-intercept form of the equation of a line to find the y-intercept.

#### Answer

Use the formula $b = y_1 - m x_1$

##### Answer for screen readers

The final answer is the y-intercept calculated using the formula $b = y_1 - m x_1$

#### Steps to Solve

["1. **Calculate the slope (m) using two points**\n\nGiven two points $(x_1, y_1)$ and $(x_2, y_2)$, the slope (m) can be calculated using the formula:\n\n$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$\n\n2. **Use the slope-intercept form of the equation**\n\nThe slope-intercept form of a linear equation is: $$ y = mx + b $$ where $m$ is the slope and $b$ is the y-intercept.\n\n3. **Substitute one point and the slope into the equation**\n\nChoose one of the given points, say $(x_1, y_1)$. Substitute this point and the slope $m$ into the equation:\n$$ y_1 = m x_1 + b $$\n\n4. **Solve for the y-intercept (b)**\n\nRearrange the equation to solve for $b$:\n$$ b = y_1 - m x_1 $$"]

The final answer is the y-intercept calculated using the formula $b = y_1 - m x_1$

#### More Information

This method uses the basic principles of linear equations and is an essential technique in algebra.

#### Tips

A common mistake is mixing up the coordinates of the points or the slope formula. Always double-check your values.