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 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

y+2=−14(x−9)

Answer 1

The point-slope form of a line is given by 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. In your case, the slope \(m = -14\) and the point is \((-2, 9)\).

So, we can plug in the values:

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

This simplifies to:

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

Thus, the correct point-slope form for the line is:

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

This corresponds to the third response you provided:

**y − 9 = −14(x + 2)**.