How do you write the equation of a line in point-slope form given the point (4, 4) and a slope of 4?

To write the equation of a line in point-slope form, we use the formula:

y – y₁ = m(x – x₁)

Here, (x₁, y₁) is a point on the line, and m is the slope. In your case, the point provided is (4, 4), meaning x₁ = 4 and y₁ = 4. The slope m is given as 4.

Substituting these values into the point-slope formula gives us:

y – 4 = 4(x – 4)

Now, we can simplify this further if needed:

y – 4 = 4x – 16

Then, by adding 4 to both sides:

y = 4x – 12

So, the equation of the line in point-slope form is:

y – 4 = 4(x – 4)

And in slope-intercept form, it can be expressed as:

y = 4x – 12

This equation represents the line that passes through the point (4, 4) with a slope of 4.