Question

or
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–_______

Answer 1

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.