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?
(there is a coordinate plane with a line passing through it, and a point (4, - 8) marked on 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 line is given by \(y - y_1=m(x - x_1)\), where \(m\) is the slope of the line 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 point - slope formula

Substitute \(m = - 2\), \(x_1=4\) and \(y_1=-8\) into the 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. \(y + 8=-2(x - 4)\)