Question

which equation represents the graphed function?\
\\(\circ\\) \\(y = -3x + 3\\)\
\\(\circ\\) \\(y = 3x - 3\\)\
\\(\circ\\) \\(y = 3x - \frac{1}{3}\\)\
\\(\circ\\) \\(y = -\frac{1}{3}x + 3\\)

Explanation:

Step1: Find the slope

Using the two points \((0, 3)\) and \((3, 2)\), the slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{2 - 3}{3 - 0}=\frac{-1}{3}=-\frac{1}{3}\).

Step2: Identify the y-intercept

The y - intercept \(b\) is the value of \(y\) when \(x = 0\). From the point \((0, 3)\), we have \(b = 3\).

Step3: Write the equation

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m =-\frac{1}{3}\) and \(b = 3\), we get \(y=-\frac{1}{3}x+3\).

Answer:

\(y =-\frac{1}{3}x + 3\) (the fourth option: \(y=-\frac{1}{3}x + 3\))