Question

Find the equation of the line.
Use exact numbers

Answer 1

y =
`(2)/(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) )`

with (x₁, y₁ ) = (- 6, 0) and (x₂, y₂ ) = (0, 4) ← 2 points on the line

m =
`(4-0)/(0-(-6))` =
`(4)/(0+6)` =
`(4)/(6)` =
`(2)/(3)`

the line crosses the y- axis at (0, 4 ) ⇒ c = 4

y =
`(2)/(3)` x + 4 ← equation of line