What is the equation of the line that passes through the points (0, 2) and (4, 6)?

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To find the equation of the line that passes through the points (0, 2) and (4, 6), we can follow these steps:

  1. Identify the points: We have two points: (x1, y1) = (0, 2) and (x2, y2) = (4, 6).
  2. Calculate the slope (m): The slope of a line through two points is given by the formula:
m = (y2 - y1) / (x2 - x1)

Substituting the values:

m = (6 - 2) / (4 - 0) = 4 / 4 = 1
  1. Use point-slope form: With the slope known, we can use the point-slope form of the equation of the line, which is:
y - y1 = m(x - x1)

Choosing the point (0, 2):

y - 2 = 1(x - 0)

Which simplifies to:

y - 2 = x

Rearranging gives us:

y = x + 2

This is the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

Conclusion: The equation of the line that passes through the points (0, 2) and (4, 6) is:

y = x + 2

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