Question

Three different proportional relationships between the quantities of $x$ and $y$ are given as below.
A: $10y=16x$
B: It represents the table below:

$x$	5	10	20
$y$	6	12	24

C: It represents the graph below:


Which is the correct ascending order of their slopes?

Answer 1

$\text{Detailed step-by-step solution:}$
$\text{Finding the slope of A:}$
$10y=16x$
$\Rightarrow y=\frac{16}{10}x$
Slope of A $=\frac{y}{x}=\frac{16}{10}($for the equation $y=mx$, the slope $=m=\frac{y}{x})$
$=1.6$

$\text{Finding the slope of B:}$
Slope of B $=\frac{\text{Change in y}}{\text{Change in x}}$
$=\frac{24-12}{20-10}$ (any two points on the table can be considered for slope calculation)
$=\frac{12}{10}$
$=1.2$

$\text{Finding the slope of C:}$
Let’s consider two points $(4,6)$ and $(2,3)$ on the graph.
Slope of the graph $=\frac{\text{Rise}}{\text{Run}}$
$=\frac{\text{Change in y}}{\text{Change in x}}$
$=\frac{6-3}{4-2}$
$=\frac{3}{2}$
$=1.5$
Since $1.2<1.5<1.6,$
$\text{Slope of B < Slope of C < Slope of A.}$
➡Option B is correct.