Step 1: Understanding the Concept
For a first order reaction, Rate \(=k[A]\).
Step 2: Compare with a straight line
This has the form \(y=mx\), with rate on the y-axis, \([A]\) on the x-axis and slope \(m=k\).
Since \(k>0\), the slope is positive and there is no intercept.
Step 3: Compare the options
A straight line through the origin with positive slope matches the third option.
Final Answer:
The graph is a straight line through the origin with positive slope.
\[ \boxed{\text{(C) }\text{A straight line passing through the origin having +ve slope}} \]