Question

Which of the following equations represent the given data about the area of the land required for the construction of a number of buildings?

Number of buildings $\left(x\right)$	$8$	$12$
Area of the land (acres) $\left(y\right)$	$10$	$15$

• A. $y=1.25x$
• B. $y=0.75x$
• C. $y=1.75x$
• D. $y=2.5x$

Answer 1

The correct option is A $y=1.25x$

We have the two sets of points in the table: $(8,10)$, and $(12,15)$.
From the given table,$\frac{y}{x}=\frac{10}{8}=\frac{5}{4}$

Also, $\frac{y}{x}=\frac{15}{12}=\frac{5}{4}$

Hence the given table represents a proportional relationship. So, equation representing this must be of the form
$y=kx$, where $k$ represents the constant of proportionality, which is $\frac{5}{4}$

So, equation of the graph is $y=\frac{5}{4}\times x$

$\Rightarrow y=1.25x$