Question

The equation that shows a proportional relationship between "x" and "y" is:

• A. y = 4x + 5
• B. y = 4x + 4
• C. y = 3x
• D. y = 2x + 3

Answer 1

The correct option is C y = 3x

The line of a proportional equation should pass through the origin (0, 0).

So, in a proportional equation:
If $x=0$, then $y=0$

Checking the value of "$y$" for $x=0$ in each equation,

Equation	Value of "$y$" at $x=0$
$y=4x+4$	$y=4\times 0+4\Rightarrow y=4$
$y=4x+5$	$y=4\times 0+5\Rightarrow y=5$
$y=2x+3$	$y=2\times 0+3\Rightarrow y=3$
$y=3x+0$	$y=3\times 0\Rightarrow y=0$

Hence, the only equation that gives $y=0$ for $x=0$ is $y=3x$

Also from the graph of the equation $y=3x$, you can see that the straight line passes through the origin (0, 0).


∴ The equation that shows a proportional relationship between "$x$" and "$y$" is $y=3x$