Question

The graph will have a positive slope if the constant of proportionality is ______.

• A. Negative
• B. Zero
• C. Greater than 1
• D. Positive

Answer 1

The correct option is D Positive

A positive slope means that as a line on the line graph moves from left to right, the line rises.

It means that if x increases, y will also increase.
Slope $=\frac{\text{Rise}}{\text{Run}}$
$=\frac{\text{Positive change in y}}{\text{Positive change in x}}$
= Slope $=\frac{b-0}{a-0}$
Constant of proportionality, $m=\frac{y}{x}$
$\Rightarrow m=\frac{b}{a}$ (substituting for x = a, y = b)
Constant of proportionality = Slope of the graph
Hence, the slope of the graph will be positive when the constant of proportionality is positive.