Is this the correct graph of the equation y=1/5x

Question

point 1 (0, 0) point 2 (5, 1)
?

(1 point)
Responses

No, it is not the correct graph because the ordered pair (1, 5)
is not a point on the graph of y=1/5x

Yes, it is the correct graph because the slope =5/1

Yes, it is the correct graph because the ordered pair (0, 0)
satisfies the equation and the slope m=rise/run=1/5

No, it is not the correct graph because the slope m=rise/run=1/5

Answer 1

To evaluate whether the graph of the equation \( y = \frac{1}{5}x \) is correct based on the provided points, let's go through the properties:

1. Identify Key Characteristics of the Equation:

   • The equation \( y = \frac{1}{5}x \) represents a straight line with a slope of \( \frac{1}{5} \). This means that for every 5 units you move horizontally to the right (rise), the line rises by 1 unit (run).

2. Test the Points:

   • Point 1: \( (0, 0) \)
     • Substituting \( x = 0 \) into the equation gives: \[ y = \frac{1}{5}(0) = 0 \]
     • So, this point is correct on the graph.
   • Point 2: \( (5, 1) \)
     • Substituting \( x = 5 \) into the equation gives: \[ y = \frac{1}{5}(5) = 1 \]
     • So, this point is also correct on the graph.

3. Check the Slope:

   • The slope, calculated as rise/run, is indeed \( \frac{1}{5} \), meaning it rises 1 unit for every 5 units run horizontally.

Based on this analysis, the response that most accurately represents the facts is:

Yes, it is the correct graph because the ordered pair (0, 0) satisfies the equation and the slope m=rise/run=1/5.