Compare constants of proportionality

Google Classroom

Problem

Which relationships have the same constant of proportionality between $y$y and $x$x as the following table?

$x$x	$y$y
$2$2	$7$7
$7$7	$24.5$24, point, 5
$9$9	$31.5$31, point, 5

Choose 3 answers:

Choose 3 answers:

• (Choice A, Checked, Correct)

  CORRECT (SELECTED)

  $4y=14x$4, y, equals, 14, x
• (Choice B, Incorrect)

  INCORRECT

  $3.5y=x$3, point, 5, y, equals, x

  The constant of proportionality for this relationship is $\dfrac{2}{7}$start fraction, 2, divided by, 7, end fraction.
• (Choice C, Incorrect)

  INCORRECT

  

  $\small{2}$$\small{4}$$\small{4}$$\small{8}$$\small{12}$$\small{16}$$\small{20}$$y$$x$

  This relationship has a constant of proportionality of $4$4.
• (Choice D, Checked, Correct)

  CORRECT (SELECTED)

  

  $\small{1}$$\small{2}$$\small{2}$$\small{4}$$\small{6}$$\small{8}$$\small{10}$$y$$x$
• (Choice E, Checked, Correct)

  CORRECT (SELECTED)

  

  $\small{2}$$\small{4}$$\small{4}$$\small{8}$$\small{12}$$\small{16}$$\small{20}$$y$$x$

Hint #11 / 7

The given table has a constant of proportionality equal to $3.5$3, point, 5.

This means that all $y$y-values in this relationship are $3.5$3, point, 5 of the $x$x-value.

Which other relationships have the same constant of proportionality?

Hint #22 / 7

Let's pick a pair of corresponding $\greenD{x}$start color #1fab54, x, end color #1fab54- and $\maroonD{y}$start color #ca337c, y, end color #ca337c-values from the table. We can use $\greenD{x}=\greenD{2}$start color #1fab54, x, end color #1fab54, equals, start color #1fab54, 2, end color #1fab54 and $\maroonD{y}=\maroonD{7}$start color #ca337c, y, end color #ca337c, equals, start color #ca337c, 7, end color #ca337c.

Let's see whether that pair makes the equation $4\maroonD{y}=14\greenD{x}$4, start color #ca337c, y, end color #ca337c, equals, 14, start color #1fab54, x, end color #1fab54 true.

$4\cdot \maroonD{7}\stackrel{\checkmark}{=}14\cdot \greenD{2}$4, dot, start color #ca337c, 7, end color #ca337c, equals, start superscript, \checkmark, end superscript, 14, dot, start color #1fab54, 2, end color #1fab54

The equation has the same constant of proportionality.

Hint #33 / 7

Let's try the pair $\greenD{x}=\greenD{2}$start color #1fab54, x, end color #1fab54, equals, start color #1fab54, 2, end color #1fab54 and $\maroonD{y}=\maroonD{7}$start color #ca337c, y, end color #ca337c, equals, start color #ca337c, 7, end color #ca337c in the equation $3.5\maroonD{y}=\greenD{x}$3, point, 5, start color #ca337c, y, end color #ca337c, equals, start color #1fab54, x, end color #1fab54, too. Does that pair of values make the equation true?

$3.5\cdot \maroonD{7}\neq\greenD{2}$3, point, 5, dot, start color #ca337c, 7, end color #ca337c, does not equal, start color #1fab54, 2, end color #1fab54

The equation $3.5\maroonD{y}=\greenD{x}$3, point, 5, start color #ca337c, y, end color #ca337c, equals, start color #1fab54, x, end color #1fab54 does not have the same constant of proportionality as the table.

Hint #44 / 7

$\small{2}$$\small{4}$$\small{4}$$\small{8}$$\small{12}$$\small{16}$$\small{20}$$y$$x$$(\greenD{1},\maroonD{4})$

Let's pick a point on the line to figure out the constant of proportionality. For the point $(\greenD{1},\maroonD{4})$left parenthesis, start color #1fab54, 1, end color #1fab54, comma, start color #ca337c, 4, end color #ca337c, right parenthesis, the $\maroonD{y}$start color #ca337c, y, end color #ca337c-value is $4$4 times the $\greenD{x}$start color #1fab54, x, end color #1fab54-value. The other points have the same relationship.

This relationship shows a constant of proportionality of $4$4 instead of $3.5$3, point, 5.

Hint #55 / 7

$\small{1}$$\small{2}$$\small{2}$$\small{4}$$\small{6}$$\small{8}$$\small{10}$$y$$x$$(\greenD{2},\maroonD{7})$

Let's pick a point from this graph, too. For the point $(\greenD{2},\maroonD{7})$left parenthesis, start color #1fab54, 2, end color #1fab54, comma, start color #ca337c, 7, end color #ca337c, right parenthesis, the $\maroonD{y}$start color #ca337c, y, end color #ca337c-value is $3.5$3, point, 5 times the $\greenD{x}$start color #1fab54, x, end color #1fab54-value. The other points have the same relationship.

This graph has a constant of proportionality of $3.5$3, point, 5.

Hint #66 / 7

$\small{2}$$\small{4}$$\small{4}$$\small{8}$$\small{12}$$\small{16}$$\small{20}$$y$$x$$(\greenD{4},\maroonD{14})$

Let's pick a point from this graph, too. For the point $(\greenD{4},\maroonD{14})$left parenthesis, start color #1fab54, 4, end color #1fab54, comma, start color #ca337c, 14, end color #ca337c, right parenthesis, the $\maroonD{y}$start color #ca337c, y, end color #ca337c-value is $3.5$3, point, 5 times the $\greenD{x}$start color #1fab54, x, end color #1fab54-value. The other points have the same relationship.

This graph has a constant of proportionality of $3.5$3, point, 5, too.

Hint #77 / 7

These are the relationships that have the same constant of proportionality between $y$y and $x$x as the given table:

$4y=14x$4, y, equals, 14, x

$\small{1}$$\small{2}$$\small{2}$$\small{4}$$\small{6}$$\small{8}$$\small{10}$$y$$x$