What is the point-slope form of a line that has a slope of 3 and passes through the point (–1, 4)?

y – (–1) = 5(x – 4)
4 – y1 = 3(–1 – x1)
y – 3 = –1[(x – (–4)]
y – 4 = 3[(x – (–1)]

1 answer

The point-slope form of a line is given by the formula:

\[ y - y_1 = m(x - x_1) \]

where \((x_1, y_1)\) is a point on the line and \(m\) is the slope.

In your case, the slope \(m\) is 3, and the point \((x_1, y_1)\) is \((-1, 4)\). Plugging these values into the formula, we get:

\[ y - 4 = 3(x - (-1)) \]

This simplifies to:

\[ y - 4 = 3(x + 1) \]

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

\[ y - 4 = 3(x + 1) \]

None of the options you provided exactly matches this correct form, but the closest rearranged version is:

Correct answer: \(y - 4 = 3(x - (-1))\) (this is the correct point-slope form translated from the equation).