How can I find the equation of the line that passes through the point (4, 3) with a slope of 12?

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

y – y1 = m(x – x1)

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

In your case, the line passes through the point (4, 3), so:

  • x1 = 4
  • y1 = 3
  • m = 12

Plugging these values into the point-slope form gives:

y – 3 = 12(x – 4)

Now, let’s simplify this equation:

  1. Distribute 12 on the right side:
  2. y – 3 = 12x – 48
  3. Next, add 3 to both sides:
  4. y = 12x – 48 + 3
  5. y = 12x – 45

Therefore, the equation of the line that passes through the point (4, 3) with a slope of 12 is:

y = 12x – 45

This linear equation describes a straight line that rises steeply because of the large slope value. You can sketch this line on a graph by plotting the point (4, 3) and another point based on the equation.

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