Constant of proportionality from graphs

Google Classroom

Problem

Lines $A$A, $B$B, and $C$C show proportional relationships.

Which line has a constant of proportionality between $y$y and $x$x of $\dfrac{1}{2}$start fraction, 1, divided by, 2, end fraction?

$\small{2}$$\small{4}$$\small{6}$$\small{2}$$\small{4}$$\small{6}$$y$$x$$A$$B$$C$

Choose 1 answer:

Choose 1 answer:

• (Choice A, Incorrect)

  INCORRECT

  $\blueD{A}$start color #11accd, A, end color #11accd
• (Choice B, Incorrect)

  INCORRECT

  $\greenD{B}$start color #1fab54, B, end color #1fab54
• (Choice C, Checked, Correct)

  CORRECT (SELECTED)

  $\purpleD{C}$start color #7854ab, C, end color #7854ab

Hint #11 / 4

The constant of proportionality is the value of $y$y when $x=1$x, equals, 1 in a proportional relationship.

On which line does $y=\dfrac{1}{2}$y, equals, start fraction, 1, divided by, 2, end fraction when $x=1$x, equals, 1?

Hint #22 / 4

Only line $\purpleD{C}$start color #7854ab, C, end color #7854ab has a $y$y-value less than $1$1 when $x=1$x, equals, 1, but how can we be sure that the constant of proportionality is exactly $\dfrac{1}{2}$start fraction, 1, divided by, 2, end fraction?

If the constant of proportionality of a proportional relationship is $\tealD{\dfrac{1}{2}}$start color #01a995, start fraction, 1, divided by, 2, end fraction, end color #01a995, then:

$\maroonD{y}=\tealD{\dfrac{1}{2}}\goldD{x}$start color #ca337c, y, end color #ca337c, equals, start color #01a995, start fraction, 1, divided by, 2, end fraction, end color #01a995, start color #e07d10, x, end color #e07d10

Let's pick a point on the graph of line $\purpleD{C}$start color #7854ab, C, end color #7854ab to get the $\goldD{x}$start color #e07d10, x, end color #e07d10- and $\maroonD{y}$start color #ca337c, y, end color #ca337c-values. Then we can test our equation.

Hint #33 / 4

$\small{2}$$\small{4}$$\small{6}$$\small{2}$$\small{4}$$\small{6}$$y$$x$$A$$B$$C$$(\goldD{2},\maroonD{1})$

We can try the point $(\goldD{2},\maroonD{1})$left parenthesis, start color #e07d10, 2, end color #e07d10, comma, start color #ca337c, 1, end color #ca337c, right parenthesis.

$\maroonD{1}\stackrel{\checkmark}{=}\tealD{\dfrac{1}{2}}(\goldD{2})$start color #ca337c, 1, end color #ca337c, equals, start superscript, \checkmark, end superscript, start color #01a995, start fraction, 1, divided by, 2, end fraction, end color #01a995, left parenthesis, start color #e07d10, 2, end color #e07d10, right parenthesis

Hint #44 / 4

Line $\purpleD{C}$start color #7854ab, C, end color #7854ab has a constant of proportionality of $\dfrac{1}{2}$start fraction, 1, divided by, 2, end fraction between $x$x and $y$y.