What is the equation of a line that goes through the point (4, 3) with a slope of 2?

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To find the equation of a line that passes through a specific point with a given slope, we can use the point-slope form of the equation of a line, which is:

y - y_1 = m(x - x_1)

In this formula:

  • (x1, y1) is the given point on the line, which is (4, 3) in this case.
  • m is the slope of the line, which is 2.

Now, we can substitute the values into the point-slope form:

y - 3 = 2(x - 4)

Next, we simplify the equation:

  1. Distributing the slope (2) to (x – 4):
    2. y - 3 = 2x - 8
  2. Now, we’ll add 3 to both sides to isolate y:
    3. y = 2x - 8 + 3
  3. This simplifies to:
    4. y = 2x - 5

Thus, the equation of the line that passes through the point (4, 3) with a slope of 2 is:

y = 2x - 5

This linear equation can be used to describe the relationship between x and y for any point on that line.

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