Question

Write the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.

Answer 1

y =
`(1)/(3)` x

Explanation:

the equation of the line through the origin is

y = mx ( m is the slope )

to calculate m use the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

let (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (6, 2) ← 2 points on the line

substitute these values into the formula for m

m =
`(2-0)/(6-0)` =
`(2)/(6)` =
`(1)/(3)`

y =
`(1)/(3)` x ← proportional relationship