Question

Thomas graphed the line that represents the equation y=34x.

Which ordered pairs represent points on the line?

Select all that apply.

(8,1/6)
(−2/3,1/2)
(4,3)
(2,3/2)
(−8,−6)

Answer 1

The ordered pairs represent points on the line are

(4, 3) ⇒ C

(2,
`(3)/(2)` ) ⇒ D

(-8, -6) ⇒ E

Explanation:

To find the ordered pairs represent points on the line, substitute x by the x-coordinate of each point, if the value of y equals the y-coordinate of the point, then the point is on the line.

∵ The equation is y =
`(3)/(4)` x

∵ The ordered pair is (8,
`(1)/(6)` )

→ Substitute x by 8

∴ y =
`(3)/(4)` (8)

∴ y = 6

∵ The value of y does not equal the y-coordinate of the ordered pair

∴ The ordered pair (8,
`(1)/(6)` ) does not represent a point on the line

∵ The ordered pair is (
`(-2)/(3)`,
`(1)/(2)` )

→ Substitute x by
`(-2)/(3)`

∴ y =
`(3)/(4)` (
`(-2)/(3)`)

∴ y =
`(-1)/(2)`

∵ The value of y does not equal the y-coordinate of the ordered pair

∴ The ordered pair (
`(-2)/(3)`,
`(1)/(2)` ) does not represent a point on the line

∵ The ordered pair is (4, 3 )

→ Substitute x by 4

∴ y =
`(3)/(4)` (4)

∴ y = 3

∵ The value of y equal the y-coordinate of the ordered pair

∴ The ordered pair (4, 3) represents a point on the line

∵ The ordered pair is (2,
`(3)/(2)` )

→ Substitute x by 2

∴ y =
`(3)/(4)` (2)

∴ y =
`(3)/(2)`

∵ The value of y equal the y-coordinate of the ordered pair

∴ The ordered pair (2,
`(3)/(2)` ) represents a point on the line

∵ The ordered pair is (-8, -6 )

→ Substitute x by -8

∴ y =
`(3)/(4)` (-8)

∴ y = -6

∵ The value of y equal the y-coordinate of the ordered pair

∴ The ordered pair (-8, -6) represents a point on the line