Question

Write in standard form: a line through the origin with slope 2/3

Answer 1

2x - 3y = 0

Explanation:

the equation of a line passing through the origin is

y = mx ( m is the slope )

here m =
`(2)/(3)` , then

y =
`(2)/(3)` x ( multiply through by 3 to clear the fraction )

3y = 2x

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

rearranging the above equation into this form

2x = 3y ( subtract 3y from both sides )

2x - 3y = 0 ← in standard form

Answer 2

y = 2/3x

Explanation:

Slope-intercept formula: y = mx + b

m = 2/3 because the slope is 2/3.

b = 0 because the y value of the origin is 0, as the point is at (0, 0).

That makes y = 2/3x + 0, but adding zero does nothing so you take it out to get y = 2/3x.