Question

Choose the correct answer.

1. What is the equation of a line that passes
through the origin and intersects (4, 6)?
A. y = -3/2x
B. y = -2/3x
C. y = 2/3x
D. y = 3/2x

Answer 1

The equation of the line is y =
`(3)/(2)` x ⇒ D

Explanation:

The form of the linear equation is y = m x + b, where

• m is the slope of the line

• b is the y-intercept (value y at x = 0)

The rule of the slope is m =
`(y2-y1)/(x2-x1)` , where

• (x1, y1) and (x2, y2) are two points on the line

∵ The line passes through the origin (0, 0) and point (4, 6)

∴ x1 = 0 and y1 = 0

∴ x2 = 4 and y2 = 6

→ Substitute them in the rule of the slope above to find it

∵ m =
`(6-0)/(4-0)=(6)/(4)=(3)/(2)`

∴ m =
`(3)/(2)`

→ Substitute it in the form of the equation above

∴ y =
`(3)/(2)` x + b

∵ The line passes through the origin

∴ The y-intercept = 0

∴ b = 0

→ Substitute it in the equation

∵ y =
`(3)/(2)` x + 0

∴ y =
`(3)/(2)` x

∴ The equation of the line is y =
`(3)/(2)` x