Question

Write the equation of the line in point-slope form using the indicated point.

Answer 1

y + 6 = -
`(3)/(4)` (x - 4)

Explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

m is the slope and (a, b ) a point on the line

calculate m using the slope formula

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

let (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (4, - 6) ← 2 points on the line

substitute these values into the formula for m

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

using (a, b ) = (4, - 6 ) , then

y - (- 6) = -
`(3)/(4)` (x - 4) , that is

y + 6 = -
`(3)/(4)` (x - 4)