ANSWER
The rate of change is
\(5\)
EXPLANATION.
The rate of change of the graph of the direct variation is the constant of variation or constant of proportionality.
In other words, the rate of change is the slope of the graph.
We can read from the graph that, the straight line passes through,
\(
(0,0) \: and \: (10,50)\)
Recall that,
\(Slope = \frac{y_2 - y_1 }{ x_2 - x_1}\)
We apply this formula to obtain,
\(Slope = \frac{50 - 0 }{ 10 - 0}\)
We simplify to obtain,
\(Slope = \frac{50 }{ 10 }\)
We simplify further to get,
\(Slope = 5\)
Therefore the rate of change of the direct variation is
\(5\)
The correct answer is option A.
