How do I find the equation of a line with a slope of 7 that passes through the point (3, 4)?

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

y - y1 = m(x - x1)

In this formula:

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

We are given a slope m = 7 and a point (x1, y1) = (3, 4).

Substituting the given values into the point-slope formula:

y - 4 = 7(x - 3)

Now, let’s simplify this equation:

  1. Distribute 7 on the right side:
    2. y - 4 = 7x - 21
  2. Add 4 to both sides to isolate y:
    3. y = 7x - 21 + 4
    y = 7x - 17

So, the equation of the line with a slope of 7 that passes through the point (3, 4) is:

y = 7x - 17

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