Question

Which of the following statements is true about the following graph?

• A. The constant of proportionality can’t be determined.
  
• B. The constant of proportionality is negative.
  
• C. The constant of proportionality is positive.
  
• D. The constant of proportionality is zero.
  

Answer 1

The correct option is B The constant of proportionality is negative.


Let’s find the equation of the straight line.


We already know two points on the graph, $(0,5)$ and $(4,0)$.

From this, we can find the slope of the line $=\frac{0-5}{4-0}=-\frac{5}{4}$

Therefore, the equation of the line must be
$y=(-\frac{5}{4})x+b$ (where $b$ is a constant)
For now, we don’t have to figure out what $b$ is. This looks very similar to the equation of a proportional relationship
$y=ax.$

Here, $a=-\frac{5}{4}$

Therefore, the constant of proportionality is negative for the given graph.