How to find the y-intercept with two points?
Understand the Problem
The question is asking how to calculate the y-intercept of a line defined by two given points. To find the y-intercept, we can determine the slope of the line using the two points and then use the slope-intercept form of the line equation (y = mx + b) to solve for the y-intercept (b).
Answer
Find the slope using $m = \frac{y_2 - y_1}{x_2 - x_1}$, and solve for $b$ with $b = y - mx$.
Answer for screen readers
To find the y-intercept, follow these steps: Find the slope using the two points, use one of the points in the slope-intercept form, and solve for b.
Steps to Solve
- Find the slope (m) of the line
Use the formula for slope $m = \frac{y_2 - y_1}{x_2 - x_1}$ where $(x_1, y_1)$ and $(x_2, y_2)$ are the given points.
- Use the slope-intercept form of the line (y = mx + b)
After finding the slope, use the equation $y = mx + b$, where $m$ is the slope and $(x, y)$ is one of the given points. Substitute the values of $x$, $y$, and $m$ into the equation.
- Solve for the y-intercept (b)
Rearrange the equation to isolate $b$. Thus $b = y - mx$.
- Write the final equation of the line
The final equation of the line will be $y = mx + b$, with the $b$ you found in the previous step.
To find the y-intercept, follow these steps: Find the slope using the two points, use one of the points in the slope-intercept form, and solve for b.
More Information
The y-intercept is the point where the line crosses the y-axis. It's important in graphing as it gives a starting point.
Tips
A common mistake is not correctly calculating the slope using the formula. Ensure to subtract the coordinates in the correct order.