Question

Which of point-slope equations below is correcto for the line that passes through points (-1,-4) and (3,2)?. Check all that apply.

Answer 1

A and E

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 ) = (- 1, - 4 ) and (x₂, y₂ ) = (3, 2 )

m =
`(2+4)/(3+1)` =
`(6)/(4)` =
`(3)/(2)`

using (a, b ) = (- 1, - 4 ), then

y + 4 =
`(3)/(2)`(x + 1 ) → A

using (a, b) = (3, 2 ), then

y - 2 =
`(3)/(2)`(x - 3 ) → E