Question

solving a linear-linear equation using a system
what lines would you use to solve
$-3x - 2 = 2x + 8$?
graph the line for the left side of the equation
graph the line a
b
c
d for the right side of the equation

Explanation:

Step1: Analyze left side function

The left side of the equation is \( y = -3x - 2 \). This is a linear function with slope \(-3\) (negative, steep negative slope) and y - intercept \(-2\). Looking at the graph, we need to find the line with slope \(-3\) and y - intercept \(-2\). Let's check the lines:

• Line D: Let's assume we can see from the graph (by checking slope and intercept) that line D has the equation \( y=-3x - 2\) (since slope is - 3 and when \(x = 0,y=-2\) which matches the left - hand side function).

Step2: Analyze right side function

The right side of the equation is \( y = 2x+8\). This is a linear function with slope \(2\) (positive slope) and y - intercept \(8\). Looking at the graph, line A has a positive slope and when we check the y - intercept (by looking at the graph), it should match \(y = 2x + 8\) (slope 2, y - intercept 8).

Answer:

For the left side of the equation (\(y=-3x - 2\)), we use line D. For the right side of the equation (\(y = 2x+8\)), we use line A. So the answers are:
Graph the line D for the left side of the equation.
Graph the line A for the right side of the equation.