# 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.

Follow the steps to calculate the y-intercept: find the slope, use point-slope form, and solve for 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.

#### Steps to Solve

1. 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:

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

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 $x = 0$.

1. Convert the equation to slope-intercept form

Convert the equation to the slope-intercept form $y = mx + b$ to easily identify the y-intercept $b$.

1. 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.