Question

Which equation represents the line that passes through the points (6,-3) and (-4,-9)

Y+4= 3/5 (x+9)
y+4= 5/3 (x+9)
y-3= 3/5 (x+6)
y+3= 3/5 (x-6)

Answer 1

D

Explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (6, - 3) and (x₂, y₂ ) = (- 4, - 9)

m =
`(-9+3)/(-4-6)` =
`(-6)/(-10)` =
`(3)/(5)`

using (- 4, - 9) or (6, - 3) for (a, b)

using (- 4, - 9), gives

y + 9 =
`(3)/(5)`(x + 4) ← not one of the options

using (6, - 3), gives

y + 3 =
`(3)/(5)`(x - 6) ← option D