Question

What is the point-slope form of the line with slope −14 that passes through the point (−2, 9)?



Responses

y+9=−14(x−2)
y plus 9 equals negative 1 fourth left parenthesis x minus 2 right parenthesis

y+2=−14(x−9)
y plus 2 equals negative 1 fourth left parenthesis x minus 9 right parenthesis

y−2=−14(x+9)
y minus 2 equals negative 1 fourth left parenthesis x plus 9 right parenthesis

y−9=−14(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 the point that the line passes through.

Given:
- Slope \( m = -14 \)
- Point \( (x_1, y_1) = (-2, 9) \)

Substituting into the point-slope form:

\[ y - 9 = -14(x - (-2)) \]

This simplifies to:

\[ y - 9 = -14(x + 2) \]

Therefore, the correct point-slope form is:

\[ y - 9 = -14(x + 2) \]

From the options given:

- \( y - 9 = -14(x + 2) \) is the correct response.

The other options do not match the correct format with the proper slope and point.