Question

Which equations can be used to represent the graph?

Answer 1

y =
`(7)/(4)` x and y = 1.75x represent the graph

Explanation:

the equation of a line passing through the origin is

y = mx ( m is the slope )

calculate the slope m using the slope formula

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

let (x₁, y₁ ) = (8, 14) and (x₂, y₂ ) = (16, 28) ← 2 points on the line

substitute these values into the formula for m

m =
`(28-14)/(16-8)` =
`(14)/(8)` =
`(7)/(4)` , then

y =
`(7)/(4)` x ← equation of line

note that
`(7)/(4)` = 7 ÷ 4 = 1.75 , then

y = 1.75x ← represents the equation of the line

the first 2 equations do not represent the equation of the line