To determine if the given graph represents the equation \( y = \frac{1}{5}x \), let's evaluate the points and the slope.
-
The points given are \( (0, 0) \) and \( (5, 1) \).
-
The ordered pair \( (0, 0) \) does satisfy the equation because if \( x = 0 \), then \( y = \frac{1}{5}(0) = 0 \).
-
Now let's check if the ordered pair \( (5, 1) \) satisfies the equation: \[ y = \frac{1}{5}(5) = 1. \] So, \( (5, 1) \) also satisfies the equation.
-
Next, calculate the slope \( m \) between the two points: \[ m = \frac{\text{rise}}{\text{run}} = \frac{1 - 0}{5 - 0} = \frac{1}{5}. \] This is the same as the slope given in the equation.
Since both points satisfy the equation \( y = \frac{1}{5}x \) and the calculated slope matches, the response to the question is:
Yes, it is the correct graph because the ordered pair (0, 0) satisfies the equation and the slope \( m = \frac{1}{5} \).