Which equation represents a line that passes through (2, 12) and has a slope of 3?

To find the equation of a line that passes through a specific point and has a given slope, we can use the point-slope form of a line’s equation. The point-slope form is expressed as:

y – y₁ = m(x – x₁)

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

In our case, the point is (2, 12) so we can substitute x₁ = 2 and y₁ = 12. The slope, m, is given as 3. Plugging these values into the equation gives us:

y - 12 = 3(x - 2)

Now, let’s simplify this equation:

y - 12 = 3x - 6

y = 3x - 6 + 12

y = 3x + 6

Thus, the equation of the line that passes through the point (2, 12) and has a slope of 3 is:

y = 3x + 6