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A line has a slope of 9 and passes through the point (
–
3,5). What is its equation in point-slope form?
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
y– ______=-_______x–_______

1 answer

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

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

Where:

  • \( m \) is the slope of the line
  • \( (x_1, y_1) \) is a point that the line passes through

Given:

  • Slope (\( m \)) = 9
  • Point (\( x_1, y_1 \)) = (–3, 5)

Substituting the values into the point-slope form:

\[ y - 5 = 9(x - (-3)) \]

This simplifies to:

\[ y - 5 = 9(x + 3) \]

So, the equation in point-slope form is:

\[ y - 5 = 9(x + 3) \]

Thus, filling in the blanks:

\[ y - 5 = -9(x - (-3)) \]

The answer can be presented as:

\[ y - 5 = 9(x + 3) \]

So, the values are:

  1. \( y_1 = 5 \)
  2. \( m = 9 \)
  3. \( x_1 = -3 \)

Thus:
\( y - 5 = 9(x + 3) \)
In the requested format:
\( y - 5 = 9(x - (-3)) \)
Here \( -(-3) = 3 \), can be expressed as \( y - 5 = 9(x - (-3)) \) for formatting purposes.