Question

question 6 (multiple choice worth 6 points) (06.02r mc) which equation does the graph of the systems of equations solve? $-\frac{1}{3}x + 3 = x - 1$ $\frac{1}{3}x - 3 = -x + 1$ $-\frac{1}{3}x + 3 = -x - 1$ $\frac{1}{3}x + 3 = x - 1$

Explanation:

Step1: Find black line equation

First, identify two points on the black line: $(0,1)$ (y-intercept, $b=1$) and $(3,-2)$. Calculate slope:
$m=\frac{-2-1}{3-0}=\frac{-3}{3}=-1$
Equation: $y=-x+1$

Step2: Find red line equation

Identify two points on the red line: $(0,-3)$ (y-intercept, $b=-3$) and $(6,-1)$. Calculate slope:
$m=\frac{-1-(-3)}{6-0}=\frac{2}{6}=\frac{1}{3}$
Equation: $y=\frac{1}{3}x-3$

Step3: Set equations equal

To find the system's solution, set the two $y$-expressions equal:
$\frac{1}{3}x-3=-x+1$

Answer:

$\boldsymbol{\frac{1}{3}x - 3 = -x + 1}$ (second option)