Question

equation of a line given point and slope

Answer 1

To find the equation of a line given a point and a slope, you can use the point-slope form of a linear equation. The point-slope form is given by:

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

where:
- \( (x_1, y_1) \) is the point on the line,
- \( m \) is the slope of the line.

Here’s how you can write the equation step-by-step:

1. Substitute the coordinates of the given point \( (x_1, y_1) \) and the slope \( m \) into the point-slope equation.
2. Simplify if necessary.

### Example:
Suppose the point is \( (2, 3) \) and the slope is \( 4 \).

1. Substitute into the point-slope form:
\[
y - 3 = 4(x - 2)
\]

2. Distribute and simplify:
\[
y - 3 = 4x - 8
\]
\[
y = 4x - 5
\]

So the equation of the line is:
\[
y = 4x - 5
\]

Feel free to provide a specific point and slope if you’d like me to work through an example with those values!