Question

The point-slope form of a line is y - y1 = m(x- x1), where m is the slope and x1
is a point on the line.

Answer 1

Yes, that's correct! The point-slope form of a linear equation is useful for writing the equation of a line when you know its slope and one point on the line.

In the equation:

- \( y \) is the dependent variable.
- \( y_1 \) is the y-coordinate of a specific point on the line (denoted as \((x_1, y_1)\)).
- \( m \) is the slope of the line, which represents the rate of change of \( y \) with respect to \( x \).
- \( x \) is the independent variable.
- \( x_1 \) is the x-coordinate of that specific point.

To use this form:

1. Identify the slope (\( m \)) of the line.
2. Choose a point on the line (\( (x_1, y_1) \)).
3. Substitute the slope and the coordinates of the point into the point-slope formula.

For example, if you have a slope of 2 and a point (3, 4) on the line, the point-slope form would be:

\[
y - 4 = 2(x - 3)
\]

If needed, you can also rearrange this into slope-intercept form (\( y = mx + b \)) or standard form (\( Ax + By = C \)).