Question

What is the point-slope form of the line with slope −1/4 that passes through the point (−2, 9)?



Responses

y+9=−1/4(x−2)
y plus 9 equals negative 1 fourth left parenthesis x minus 2 right parenthesis

y+2=−1/4(x−9)
y plus 2 equals negative 1 fourth left parenthesis x minus 9 right parenthesis

y−2=−1/4(x+9)
y minus 2 equals negative 1 fourth left parenthesis x plus 9 right parenthesis

y−9=−1/4(x+2)
y minus 9 equals negative 1 fourth left parenthesis x plus 2 right parenthesis

Answer 1

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

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

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

In this case, the slope \( m \) is \(-\frac{1}{4}\) and the point is \((-2, 9)\), so we have:

- \( x_1 = -2 \)
- \( y_1 = 9 \)

Substituting these values into the point-slope form equation gives:

\[ y - 9 = -\frac{1}{4}(x + 2) \]

Therefore, the correct option is:

**y − 9 = −1/4(x + 2)**.