Question

How do i solve this?

Answer 1

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

Explanation:

the equation of a line in slope- intercept form is

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

calculate the slope m using the slope formula

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

let (x₁, y₁ ) = (- 3, - 1) and (x₂, y₂ ) = (1, 1) ← 2 points on the line

substitute these values into the formula for m

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

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

to find c, substitute either of the 2 points into the partial equation

using (1, 1 )

1 =
`(1)/(2)`(1) + c =
`(1)/(2)` + c ( subtract
`(1)/(2)` from both sides )

1 -
`(1)/(2)` = c , that is

c =
`(1)/(2)`

y =
`(1)/(2)` x +
`(1)/(2)` ← equation of line