Question

Use the given conditions to write an equation for the line in slope-intercept form.

Passing through (-6, -6) and (-3, -5)

Answer 1

y =
`(1)/(3)` x - 4

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) )`

let (x₁, y₁ ) = (- 6, - 6 ) and (x₂, y₂ ) = (- 3, - 5 )

substitute these values into the formula for m

m =
`(-5-(-6))/(-3-(-6))` =
`(-5+6)/(-3+6)` =
`(1)/(3)` , then

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

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

using (- 6, - 6 ) for x and y

- 6 =
`(1)/(3)` (- 6) + c = - 2 + c ( add 2 to both sides )

- 4 = c

y =
`(1)/(3)` x - 4 ← equation of line