Question

identify the graph of the following equation.
$y = \frac{1}{3}x + 4$
choose the correct graph below.
\\(\bigcirc\\) a.
\\(\bigcirc\\) b.
\\(\bigcirc\\) c.
\\(\bigcirc\\) d.

Explanation:

Step1: Analyze the slope and y-intercept

The equation \( y = \frac{1}{3}x + 4 \) is in slope - intercept form \( y=mx + b \), where \( m=\frac{1}{3} \) (slope) and \( b = 4 \) (y - intercept). A positive slope means the line rises from left to right. The y - intercept is 4, so the line crosses the y - axis at \( (0,4) \).

Step2: Evaluate the options

• Option B: Has a negative slope (falls from left to right), so it's incorrect.
• Option C: The y - intercept seems to be around 0 or negative, not 4, and the slope is steeper than \( \frac{1}{3} \), so it's incorrect.
• Option D: Is a horizontal line (slope = 0), so it's incorrect.
• Option A: Has a positive slope (rises from left to right) and the y - intercept is around 4 (since when \( x = 0 \), \( y=4 \)), which matches the equation \( y=\frac{1}{3}x + 4 \).

Answer:

A. (The graph in option A which has a positive - sloped line crossing the y - axis at \( y = 4 \) and rising from left to right)