How to find the y-intercept with 2 points?
Understand the Problem
The question is asking how to calculate the y-intercept of a line using two given points. The y-intercept is the point where the line crosses the y-axis, and it can be found using the coordinates of the two points to determine the slope and the equation of the line.
Answer
Follow the steps to calculate the y-intercept: find the slope, use point-slope form, and solve for b.
Answer for screen readers
To find the y-intercept of the line given two points, follow these steps: Calculate the slope using the two points, use the point-slope form of the line to find the equation, and then solve for b (the y-intercept) when x equals 0.
Steps to Solve
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Find the slope (m) of the line using the two points
Suppose the two points are $(x_1, y_1)$ and $(x_2, y_2)$. The formula to find the slope $m$ is:
$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
- Use the point-slope form of the equation of a line to find the y-intercept (b)
The point-slope form of a line's equation is:
$$ y - y_1 = m(x - x_1) $$
You can solve for $b$ (the y-intercept) by substituting $m$ (the slope) and one of the points $(x_1, y_1)$ into the equation, and then solving for $y$ when $x = 0$.
- Convert the equation to slope-intercept form
Convert the equation to the slope-intercept form $y = mx + b$ to easily identify the y-intercept $b$.
- Calculate b
Solve for $b$ by substituting $x = 0$ into the equation $y = mx + b$.
To find the y-intercept of the line given two points, follow these steps: Calculate the slope using the two points, use the point-slope form of the line to find the equation, and then solve for b (the y-intercept) when x equals 0.
More Information
The y-intercept is where the line crosses the y-axis, and it provides information about the initial value of the dependent variable in various contexts, such as economics, physics, and biology.
Tips
A common mistake is calculating the slope incorrectly by mixing up the coordinates (x1, y1) and (x2, y2). Always keep track of which point's coordinates are subtracted from which.
