What is the equation in point-slope form of the line passing through (1, 2) and (2, 5)?

To find the equation in point-slope form of the line passing through the points (1, 2) and (2, 5), we first need to determine the slope of the line.

The formula for the slope (m) between two points (x₁, y₁) and (x₂, y₂) is:

m = (y₂ – y₁) / (x₂ – x₁)

Plugging in our points (1, 2) as (x₁, y₁) and (2, 5) as (x₂, y₂):

m = (5 – 2) / (2 – 1) = 3 / 1 = 3

Now that we have the slope, we can use the point-slope form of the equation of a line, which is:

y – y₁ = m(x – x₁)

Using the point (1, 2) and the slope we just calculated (3):

y – 2 = 3(x – 1)

This is the point-slope form of the line passing through the given points.