What is the equation of the line with a slope of 4 that passes through the point (6, 11)?

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

y – y1 = m(x – x1)

Where:

  • (x1, y1) is a point on the line (in this case, (6, 11))
  • m is the slope of the line (here, it is 4)

Plugging in the slope and the coordinates of the point:

  • x1 = 6
  • y1 = 11
  • m = 4

This gives us:

y – 11 = 4(x – 6)

Now, we can simplify this equation:

  1. Distribute the 4: y – 11 = 4x – 24
  2. Add 11 to both sides: y = 4x – 24 + 11
  3. Combine the numbers: y = 4x – 13

So, the equation of the line with a slope of 4 that passes through the point (6, 11) is:

y = 4x – 13

This linear equation can now be used to analyze any other information about the line, such as its intersection with the axes or its behavior across different intervals!

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