How can you find the equation of a line with a slope of 8 and passing through the point (4, 5)?

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To find the equation of a line given a slope and a point, you can use the point-slope form of the equation of a line, which is expressed as:

y - y1 = m(x - x1)

In this equation:

  • m is the slope of the line.
  • (x1, y1) is the point through which the line passes.

In your case, the slope (m) is 8, and the point (x1, y1) is (4, 5).

Plug these values into the formula:

y - 5 = 8(x - 4)

Now, simplify the equation step-by-step:

  1. Distribute the slope (8) to both terms in the parentheses:
    2. y - 5 = 8x - 32
  1. Add 5 to both sides to isolate y:
    2. y = 8x - 32 + 5
  1. Simplify the right side:
    2. y = 8x - 27

The equation of the line with a slope of 8 that passes through the point (4, 5) is:

y = 8x - 27

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