Question

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

y + 1 = 1/2(x + 3)
y=1/2x+5/2
-x + 2y = 1
x-2y = -1

Answer 1

- x + 2y = 1

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

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (3, 2)

m =
`(2-0)/(3+1)` =
`(2)/(4)` =
`(1)/(2)`, thus

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 = 2 -
`(3)/(2)` =
`(1)/(2)`

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

Multiply through by 2

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

- x + 2y = 1 ← in standard form