Question

question 3 of 10
the slope of the line below is -2. which of the following is the point - slope
form of the line?
a. ( y + 8 = -2(x - 4) )
b. ( y + 4 = -2(x - 8) )
c. ( y - 8 = -2(x + 4) )
d. ( y - 4 = -2(x + 8) )

Explanation:

Step1: Recall Point - Slope Formula

The point - slope form of a linear equation is \( y - y_1=m(x - x_1) \), where \( m \) is the slope and \( (x_1,y_1) \) is a point on the line.

Step2: Identify \( m \), \( x_1 \), and \( y_1 \)

We are given that the slope \( m=-2 \), and the point on the line is \( (4,-8) \). So, \( x_1 = 4 \) and \( y_1=-8 \).

Step3: Substitute into the Formula

Substitute \( m=-2 \), \( x_1 = 4 \), and \( y_1=-8 \) into the point - slope formula \( y - y_1=m(x - x_1) \).
We get \( y-(-8)=-2(x - 4) \), which simplifies to \( y + 8=-2(x - 4) \).

Answer:

A. \( y + 8 = -2(x - 4) \)