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.
