Question

What is the equation of the line in standard form?

A) 3x-y=-6

B) x-6y=-9

C) x+6y=9

D) 3x+y=6​

Answer 1

B

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 1) and (x₂, y₂ ) = (3, 2)

m =
`(2-1)/(3+3)` =
`(1)/(6)`, thus

y =
`(1)/(6)` x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (3, 2), then

2 =
`(1)/(2)` + c ⇒ c =
`(3)/(2)`, thus

y =
`(1)/(6)` x +
`(3)/(2)` ← in slope- intercept form

Multiply through by 6

6y = x + 9 ( subtract 6y from both sides )

0 = x - 6y + 9 ( subtract 9 from both sides )

- 9 = x - 6y, that is

x - 6y = - 9 ← in standard form → B