Compare constants of proportionality

Google Classroom

Problem

Which relationships have the same constant of proportionality between $y$y and $x$x as the equation $y=\dfrac{5}{2}x$y, equals, start fraction, 5, divided by, 2, end fraction, x?

Choose 3 answers:

Choose 3 answers:

• (Choice A, Incorrect)

  INCORRECT

  $5y=2x$5, y, equals, 2, x

  This relationship has a constant of proportionality of $\dfrac{2}{5}$start fraction, 2, divided by, 5, end fraction.
• (Choice B, Checked, Correct)

  CORRECT (SELECTED)

  $8y=20x$8, y, equals, 20, x
• (Choice C, Checked, Correct)

  CORRECT (SELECTED)

  

  $\small{2}$$\small{4}$$\small{6}$$\small{2}$$\small{4}$$\small{6}$$y$$x$
• (Choice D, Incorrect)

  INCORRECT

  

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

  CORRECT (SELECTED)

  $x$x	$y$y
  $1$1	$2\dfrac{1}{2}$2, start fraction, 1, divided by, 2, end fraction
  $4$4	$10$10
  $7$7	$17\dfrac{1}{2}$17, start fraction, 1, divided by, 2, end fraction

Hint #11 / 7

The equation $y=\dfrac{5}{2}x$y, equals, start fraction, 5, divided by, 2, end fraction, x has a constant of proportionality equal to $\dfrac{5}{2}$start fraction, 5, divided by, 2, end fraction.

This means that all $y$y-values in this relationship are $\dfrac{5}{2}$start fraction, 5, divided by, 2, end fraction of the $x$x-value.

Which other relationships have the same constant of proportionality?

Hint #22 / 7

Let's pick an $\greenD{x}$start color #1fab54, x, end color #1fab54-value and the $\maroonD{y}$start color #ca337c, y, end color #ca337c-value that works with the equation.

Suppose we picked the value $\greenD{x}=\greenD{4}$start color #1fab54, x, end color #1fab54, equals, start color #1fab54, 4, end color #1fab54. That means that $\maroonD{y}=\dfrac{5}{2}\cdot \greenD{4}=\maroonD{10}$start color #ca337c, y, end color #ca337c, equals, start fraction, 5, divided by, 2, end fraction, dot, start color #1fab54, 4, end color #1fab54, equals, start color #ca337c, 10, end color #ca337c.

Let's see whether that's true for the equation $5\maroonD{y}=2\greenD{x}$5, start color #ca337c, y, end color #ca337c, equals, 2, start color #1fab54, x, end color #1fab54.

$5\cdot \maroonD{10}\neq2\cdot \greenD{4}$5, dot, start color #ca337c, 10, end color #ca337c, does not equal, 2, dot, start color #1fab54, 4, end color #1fab54

The equation does not have the same constant of proportionality.

Hint #33 / 7

Let's try the pair $\greenD{x}=\greenD{4}$start color #1fab54, x, end color #1fab54, equals, start color #1fab54, 4, end color #1fab54 and $\maroonD{y}=\maroonD{10}$start color #ca337c, y, end color #ca337c, equals, start color #ca337c, 10, end color #ca337c in the equation $8\maroonD{y}=20\greenD{x}$8, start color #ca337c, y, end color #ca337c, equals, 20, start color #1fab54, x, end color #1fab54, too. Does that pair of values make the equation true?

$8\cdot \maroonD{10}\stackrel{\checkmark}{=}20\cdot \greenD{4}$8, dot, start color #ca337c, 10, end color #ca337c, equals, start superscript, \checkmark, end superscript, 20, dot, start color #1fab54, 4, end color #1fab54

The equation $8\maroonD{y}=20\greenD{x}$8, start color #ca337c, y, end color #ca337c, equals, 20, start color #1fab54, x, end color #1fab54 has the same constant of proportionality as the original equation.

Hint #44 / 7

$\small{2}$$\small{4}$$\small{6}$$\small{2}$$\small{4}$$\small{6}$$y$$x$$(\greenD{2},\maroonD{5})$

Let's pick a point on the line to figure out the constant of proportionality. For the point $(\greenD{2},\maroonD{5})$left parenthesis, start color #1fab54, 2, end color #1fab54, comma, start color #ca337c, 5, end color #ca337c, right parenthesis, the $\maroonD{y}$start color #ca337c, y, end color #ca337c-value is $\dfrac{5}{2}$start fraction, 5, divided by, 2, end fraction of 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 $\dfrac{5}{2}$start fraction, 5, divided by, 2, end fraction.

Hint #55 / 7

$\small{2}$$\small{4}$$\small{6}$$\small{2}$$\small{4}$$\small{6}$$y$$x$$(\greenD{5},\maroonD{2})$

Let's pick a point from this graph, too. For the point $(\greenD{5},\maroonD{2})$left parenthesis, start color #1fab54, 5, end color #1fab54, comma, start color #ca337c, 2, end color #ca337c, right parenthesis, the $\maroonD{y}$start color #ca337c, y, end color #ca337c-value is $\dfrac25$start fraction, 2, divided by, 5, end fraction times the $\greenD{x}$start color #1fab54, x, end color #1fab54-value, not $\dfrac52$start fraction, 5, divided by, 2, end fraction.

The graph does not have the same constant of proportionality.

Hint #66 / 7

$x$x	$y$y
$1$1	$2\dfrac{1}{2}$2, start fraction, 1, divided by, 2, end fraction
$4$4	$10$10
$7$7	$17\dfrac{1}{2}$17, start fraction, 1, divided by, 2, end fraction

In this table, every $\maroonD{y}$start color #ca337c, y, end color #ca337c-value is $2\dfrac{1}{2}$2, start fraction, 1, divided by, 2, end fraction times its corresponding $\greenD{x}$start color #1fab54, x, end color #1fab54-value.

Since $2\dfrac{1}{2}=\dfrac{5}{2}$2, start fraction, 1, divided by, 2, end fraction, equals, start fraction, 5, divided by, 2, end fraction, the constant of proportionality for this table is also $\dfrac{5}{2}$start fraction, 5, divided by, 2, end fraction.

Hint #77 / 7

These are the relationships that have the same constant of proportionality between $y$y and $x$x as the equation $y=\dfrac{5}{2}x$y, equals, start fraction, 5, divided by, 2, end fraction, x:

$8y=20x$8, y, equals, 20, x

$\small{2}$$\small{4}$$\small{6}$$\small{2}$$\small{4}$$\small{6}$$y$$x$

$x$x	$y$y
$1$1	$2\dfrac{1}{2}$2, start fraction, 1, divided by, 2, end fraction
$4$4	$10$10
$7$7	$17\dfrac{1}{2}$17, start fraction, 1, divided by, 2, end fraction