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Write an equation in point-slope form for the line through the given point with the given slope.

(10, –9); m = –2

y – 9 = –2(x – 10)

y – 10 = –2(x + 9)

y – 9 = –2(x + 10)

y + 9 = –2(x – 10)

1 answer

To write the equation of a line in point-slope form, we use the formula:

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

Where \( (x_1, y_1) \) is the given point and \( m \) is the slope.

Given the point \( (10, -9) \) and the slope \( m = -2 \):

  • \( x_1 = 10 \)
  • \( y_1 = -9 \)
  • \( m = -2 \)

Substituting these values into the point-slope formula gives:

\[ y - (-9) = -2(x - 10) \]

This simplifies to:

\[ y + 9 = -2(x - 10) \]

Thus, the correct equation in point-slope form is:

\[ y + 9 = -2(x - 10) \]

So the correct answer from your choices is:

y + 9 = –2(x – 10)