What is the equation of a line with a slope of 4 that passes through the point (3, 8)?

by

To find the equation of a line with a given slope and a point through which it passes, we can use the point-slope form of the equation of a line. The point-slope form is expressed as:

y - y1 = m(x - x1)

In this formula:

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

In our case, the slope m is 4, and the point (x1, y1) is (3, 8). Substituting these values into the point-slope form gives us:

y - 8 = 4(x - 3)

Now, let’s simplify this equation:

  1. Distribute the 4 on the right side:
    2. y - 8 = 4x - 12
  2. Add 8 to both sides to solve for y:
    3. y = 4x - 12 + 8
  3. Combine like terms:
    4. y = 4x - 4

Thus, the equation of the line with a slope of 4 that passes through the point (3, 8) is:

y = 4x - 4

This equation can now be used to graph the line or analyze its properties further.

Leave a Comment