A line passes through the point (2, 3) and has a slope of -2. Which is the equation of the line in point-slope form?

Question

Responses
A 2x + y = 72 x + y = 7
B y = -2x + 7y = -2 x + 7
C y - 3 = -2(x - 2)y - 3 = -2( x - 2)
D y = - 1/2 x+5

x + 5y = - 1 2 x + 5
E y + 3 = -2(x + 2)

Answer 1

The point-slope form of a line is given by the equation:

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

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

For the line passing through the point \( (2, 3) \) with a slope of \( -2 \), we can substitute \( x_1 = 2 \), \( y_1 = 3 \), and \( m = -2 \) into the formula:

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

So, the correct equation in point-slope form is:

C \( y - 3 = -2(x - 2) \).