How do I write the equation of a line that passes through the points (0, 1) and (2, 5)?

Finding the Equation of a Line

To find the equation of a line that passes through two given points, we can use the point-slope form or the slope-intercept form of a line. In this case, we will first determine the slope of the line using the two points provided: (0, 1) and (2, 5).

Step 1: Calculate the Slope (m)

The slope (m) of a line that passes through two points (x₁, y₁) and (x₂, y₂) is calculated using the formula:

m = (y₂ – y₁) / (x₂ – x₁)

Plugging in our points:

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

This results in:

m = (5 – 1) / (2 – 0) = 4 / 2 = 2

Step 2: Use Point-Slope Form to Write the Equation

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 (0, 1) and the slope (2), we have:

y – 1 = 2(x – 0)

Now, simplify this equation:

y – 1 = 2x

y = 2x + 1

Final Equation

The equation of the line that passes through the points (0, 1) and (2, 5) is:

y = 2x + 1