Question

There is a line that includes the point (5,–8) and has a slope of 2. What is its equation in point-slope form?

Answer 1

To write the equation of a line in point-slope form, you can use the formula:

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

where \((x_1, y_1)\) is a point on the line and \(m\) is the slope.

Given:
- Point \((x_1, y_1) = (5, -8)\)
- Slope \(m = 2\)

Plugging these values into the point-slope formula gives:

\[ y - (-8) = 2(x - 5) \]

This simplifies to:

\[ y + 8 = 2(x - 5) \]

So, the equation of the line in point-slope form is:

\[ y + 8 = 2(x - 5) \]