What is the equation of the line that passes through the points (0, 1) and (2, 3)?

To find the equation of the line that passes through the two given points, (0, 1) and (2, 3), we can follow these steps:

Step 1: Determine the Slope

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

m = (y₂ – y₁) / (x₂ – x₁)

For our points, (0, 1) and (2, 3):

• (x₁, y₁) = (0, 1)
• (x₂, y₂) = (2, 3)

Plugging in the values:

m = (3 – 1) / (2 – 0) = 2 / 2 = 1

Step 2: Use the Point-Slope Form of the Line

With the slope found, we can use the point-slope form of the equation of a line:

y – y₁ = m(x – x₁)

Substituting m = 1 and using the point (0, 1):

y – 1 = 1(x – 0)

y – 1 = x

Step 3: Rearranging to Slope-Intercept Form

Now let’s rearrange the equation to get it into slope-intercept form (y = mx + b):

y = x + 1

Conclusion

The equation of the line that passes through the points (0, 1) and (2, 3) is:

y = x + 1