Question

What is the point-slope form of a line that has a slope of –4 and passes through point (–3, 1)?
y minus (negative 3) = negative 4 (x minus 1)
y minus 1 = negative 4 left-bracket x minus (negative 3) right-bracket
Negative 1 minus y 1 = negative 4 (negative 3 minus x 1)
3 minus y 1 = negative 4 (1 minus x 1)

Answer 1

The point-slope form of a line can be expressed using the formula:

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

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

Given your slope \( m = -4 \) and the point \( (x_1, y_1) = (-3, 1) \), we can substitute these values into the point-slope form.

Substituting in the values:

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

This simplifies to:

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

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

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

Let's look at the incorrect forms you provided:

1. \( y - (-3) = -4(x - 1) \) - Incorrect, as it uses \( -3 \) as \( y_1 \) and \( 1 \) as \( x_1 \).
2. \( -1 - y_1 = -4(-3 - x_1) \) - Incorrect, as it does not adhere to the point-slope form.
3. \( 3 - y_1 = -4(1 - x_1) \) - Incorrect, as it also does not match the point-slope structure.

The correct answer is:

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