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.