Question

What is the standard form equation of the line shown below?

Answer 1

maybe

`y = (1)/(2) x + 0.5`

Answer 2

x - 2y = - 1

Explanation:

The equation of a line in standard form is

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

Obtain the equation in slope- intercept form

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) ← 2 points on the line

m =
`(2+1)/(3+3)` =
`(3)/(6)` =
`(1)/(2)`

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

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

Using (3, 2), then

2 =
`(3)/(2)` + c ⇒ c =
`(1)/(2)`

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

Multiply all terms by 2

2y = x + 1 ( subtract 2y from both sides )

0 = x - 2y + 1 ( subtract 1 from both sides )

- 1 = x - 2y , that is

x - 2y = - 1 ← in standard form