Which answer is an equation in point-slope form for the given point and slope?

Question

Point: (5, 9); Slope: 2

A. y − 5 = 2(x + 9)

B. y − 9 = 2(x − 5)

C. y − 9 = 2(x + 5)

D. y + 9 = 2(x − 5)

Answer 1

To write an equation in point-slope form, you can use the formula:

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

where \((x_1, y_1)\) is the given point and \( m \) is the slope.

For the point \((5, 9)\) and slope \(2\):

1. Here, \(x_1 = 5\), \(y_1 = 9\), and \(m = 2\).
2. Plugging these values into the point-slope formula:

\[ y - 9 = 2(x - 5) \]

So the correct choice from the options provided is:

B. y − 9 = 2(x − 5).