What is the equation of a line that passes through the point (7, 8) and has a slope of 3?

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To find the equation of a line that passes through the point (7, 8) with a slope of 3, we can use the point-slope form of the equation of a line. The point-slope form is given by the formula:

y – y1 = m(x – x1)

In this formula:

  • (x1, y1) is a point on the line, and in our case, that point is (7, 8).
  • m is the slope of the line, which is 3.

Substituting the given point and slope into the formula:

y – 8 = 3(x – 7)

Now, let’s simplify this equation step by step:

  1. Distributing 3 on the right side:

    2. y – 8 = 3x – 21

  2. Adding 8 to both sides:

    3. y = 3x – 21 + 8

    y = 3x – 13

So, the equation of the line that passes through the point (7, 8) with a slope of 3 is:

y = 3x – 13

This is the slope-intercept form of the equation, where 3 is the slope and -13 is the y-intercept.

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