Introduction
If you are wondering how to find b from two points, you are looking for the y‑intercept of a straight line that passes through the given coordinates. This article explains the concept, provides a clear step‑by‑step method, includes the underlying mathematical reasoning, and answers frequently asked questions, making it a complete guide for students and anyone needing to determine the intercept from just two points.
Steps
Calculate the slope
The first step in how to find b from two points is to determine the slope (m) of the line that connects the points ((x_1, y_1)) and ((x_2, y_2)) Simple, but easy to overlook..
[ m = \frac{y_2 - y_1}{x_2 - x_1} ]
Important: the denominator cannot be zero; if (x_2 = x_1) the line is vertical and has no y‑intercept.
Use the point‑slope form
Once the slope is known, write the equation of the line using the point‑slope form:
[ y - y_1 = m,(x - x_1) ]
This form is especially useful because it directly incorporates one of the given points and the slope you just calculated Small thing, real impact..
Solve for b
To isolate the y‑intercept b, rearrange the slope‑intercept form (y = mx + b). From the point‑slope equation, substitute (y) with the y‑coordinate of the chosen point and solve:
[ b = y_1 - m,x_1 ]
Tip: you can use either point ((x_1, y_1)) or ((x_2, y_2)); both will give the same result.
Verify the result
Finally, check your answer by plugging both original points into the completed equation (y = mx + b). If the equality holds for each point, the calculation is correct.
Example
Find b for the points ((2, 3)) and ((5, 11)) And that's really what it comes down to..
- Slope:
