Question

which graph best represents the equation of the line $y = -\frac{1}{3}x + 2$?
a
b
c
d
\bigcirc a
\bigcirc b
\bigcirc c
\bigcirc d

Explanation:

Step1: Analyze the slope and y-intercept

The equation of the line is given in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=-\frac{1}{3}x + 2\), the slope \(m=-\frac{1}{3}\) (negative, so the line should be decreasing from left to right) and the y - intercept \(b = 2\) (the line crosses the y - axis at \((0,2)\)).

Step2: Analyze each option

• Option A: The line has a negative slope and crosses the y - axis at \((0, - 2)\). The y - intercept is incorrect, so A is not correct.
• Option B: The line has a positive slope (increasing from left to right), but our slope is negative. So B is not correct.
• Option C: The slope of the line is very steep (with a large magnitude of slope), but our slope is \(-\frac{1}{3}\) (a small magnitude of slope). So C is not correct.
• Option D: The line has a negative slope (decreasing from left to right) and crosses the y - axis at \((0,2)\), which matches the slope and y - intercept of the equation \(y =-\frac{1}{3}x+2\).

Answer:

D