Question

slope of the line below is -3 use the coordinates (5, -7)to find a point slope equation

Answer 1

To write the point-slope form of the equation of a line, you can use 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.

Given:
- Slope \( m = -3 \)
- Point \( (x_1, y_1) = (5, -7) \)

Substituting these values into the formula:

\[
y - (-7) = -3(x - 5)
\]

This simplifies to:

\[
y + 7 = -3(x - 5)
\]

You can leave the equation in this form as a point-slope equation. If you want to simplify it further (but it's not necessary for the point-slope form), you could distribute the -3:

\[
y + 7 = -3x + 15
\]

Then, subtract 7 from both sides to express it in slope-intercept form:

\[
y = -3x + 15 - 7
\]

\[
y = -3x + 8
\]

However, the point-slope form \( y + 7 = -3(x - 5) \) is entirely valid, and you can use either form depending on your needs!