Question

What is the point-slope form of the equation of the line that has a slope of 2 and passes through the point (−5,4)
?

Answer 1

The point-slope form of the equation of a line is given by 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:
- Slope \(m = 2\)
- Point \((x_1, y_1) = (-5, 4)\)

Substituting these values into the point-slope formula:

\[
y - 4 = 2(x - (-5))
\]

This simplifies to:

\[
y - 4 = 2(x + 5)
\]

Therefore, the point-slope form of the equation of the line is:

\[
y - 4 = 2(x + 5)
\]