Question

Ester and Robert calculated slope for different sets of data. Ester found an equation as $3y=x$ for the given table and Robert calculated slope $=2$ for the given graph.

$x$	$1.5$	$3.5$	$7$
$y$	$4.5$	$10.5$	\$21$

Choose the correct statement.

Answer 1

Detailed step-by-step solution:
Finding the equation for the table:
Let the equation of the table be $y=mx$.
Substituting $x=1.5$ and $y=4.5$ in $y=mx$, we get:
$4.5=15m$
$\Rightarrow m=\frac{4.5}{1.5}$
$\Rightarrow m=3$
Substituting the value of $m$ in $y=mx$, we get the equation of the table.
$y=3x$
Ester is incorrect in finding the equation.
Calculating the slope of the graph:
Let’s consider two points $(4,8)$ and $(2,4)$ on the graph:
$\text{Slope}=\frac{\text{Rise}}{\text{Run}}$
$\frac{\text{Change in y}}{\text{Change in x}}$
$=\frac{8-4}{4-2}$
$=\frac{4}{2}$
$=2$
Robert is correct in calculating the slope.
Hence, Robert is correct and Ester is incorrect.
Option D is correct.