Question

Number of people eating fruits in their breakfast is given by the equation:
4y = 24x - 12.

Number of people eating bread in breakfast is given by the following graph:


Which is a more preferred breakfast?

• A. Fruits
• B. Both
• C. Can't be determined
• D. Bread

Answer 1

The correct option is A Fruits

Number of people having fruits as breakfast is given by: 4y = 24x - 12

The equation can be rearranged as: $\frac{4y}{4}=\frac{24x}{4}-\frac{12}{4}⟹y=6x-3$

The above equation is in the form of y = mx + c, where 'm' indicates the slope.

Comparing the equation y = 6x - 3 with y = mx + c, we get:

Slope (m) = 6

Now for people having bread in their breakfast:


Let us consider two points on the graph, say (0,0.5) and (0.6,3.8)

$\text{We know slope (m)}=\frac{\text{Change in y}}{\text{Change in x}}$

$=\frac{3.8-0.5}{0.6-0}$

$=\frac{3.3}{0.6}$

$=5.5$

Slope (m) = 5.5

We know, function having a greater slope represents people having that food as their more preferred brekfast.

Slope of function represeting people having fruits is more than people having fruits in their breakfast.

∴ Fruits is more preferred to bread in the breakfast.