Question

consider the graphed equation below. what is the equation of the line that passes through (-3, 2) and is parallel to the graphed equation? a y=-x + 2 b. y=-x - 1 c. y=x - 1

Explanation:

Step1: Find the slope of the graphed line

The graphed line has a slope -1 (since it goes down 1 unit for every 1 unit it goes to the right). Parallel lines have the same slope. So the slope \(m\) of the required line is - 1.

Step2: Use the point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)=(-3,2)\) and \(m=-1\). Substitute these values: \(y - 2=-1(x+3)\).

Step3: Simplify the equation

Expand the right - hand side: \(y - 2=-x - 3\). Then add 2 to both sides to get \(y=-x - 1\).

Answer:

B. \(y=-x - 1\)