What is the point-slope form equation of the line that goes through the points (0, 2) and (1, 5)?

To find the equation of the line in point-slope form that passes through the points (0, 2) and (1, 5), we first need to determine the slope of the line. The slope (m) can be calculated using the formula:

m = (y₂ – y₁) / (x₂ – x₁)

In our case:

• (x₁, y₁) = (0, 2)
• (x₂, y₂) = (1, 5)

Substituting these values in:

m = (5 – 2) / (1 – 0) = 3 / 1 = 3

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

y – y₁ = m(x – x₁)

Using the point (0, 2) and the slope we calculated:

y – 2 = 3(x – 0)

This simplifies to:

y – 2 = 3x

And if we want to express this as:

y = 3x + 2

So, the equation of the line in point-slope form is y – 2 = 3(x – 0).