Question

look at the equation below.
$y = -\frac{1}{3}x + 2$
which graph represents the equation?

Explanation:

Step1: Analyze the equation form

The equation is \( y = -\frac{1}{3}x + 2 \), which is in slope - intercept form \( y=mx + b \), where \( m =-\frac{1}{3}\) (slope) and \( b = 2 \) (y - intercept).

Step2: Identify key features

• Y - intercept: The line should cross the y - axis at \( (0,2) \).
• Slope: The slope \( m=-\frac{1}{3}\) means that for every 3 units we move to the right (increase in x by 3), we move down 1 unit (decrease in y by 1), or for every 3 units we move to the left (decrease in x by 3), we move up 1 unit (increase in y by 1).

We would look for a line that crosses the y - axis at \( (0,2) \) and has a negative, relatively shallow slope (since the absolute value of the slope \( \frac{1}{3}<1 \)).

(Note: Since the graphs are not visible here, but the process to identify the correct graph is as above. If we had the graphs, we would check for the y - intercept at (0,2) and the slope of - 1/3.)

Answer:

(To be determined by checking the graphs for y - intercept at (0,2) and slope - 1/3. For example, if there are three graphs, say Graph A, Graph B, Graph C: if Graph B has y - intercept at (0,2) and a slope of - 1/3, then the answer would be B. Graph B)