What is the equation of a line that passes through the point (2, 12) with a slope of 3?

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Finding the Equation of a Line

To find the equation of a line, we can use the point-slope form of a linear equation, which is given by:

y - y1 = m(x - x1)

In this equation:

  • m is the slope of the line.
  • (x1, y1) is a specific point on the line.

Given that the slope (m) is 3 and the line passes through the point (2, 12), we can substitute these values into the point-slope form:

y - 12 = 3(x - 2)

Next, let’s simplify the equation:

  1. Distributing the slope on the right side:
    2. y - 12 = 3x - 6
  2. Now, we solve for y by adding 12 to both sides:
    3. y = 3x - 6 + 12
  3. This simplifies to:
    4. y = 3x + 6

Thus, the equation of the line that passes through the point (2, 12) with a slope of 3 is:

y = 3x + 6

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