Question

How do i find the equation of the line?

Answer 1

Two Point form for a line through (a,b) and (c,d) is

`(c-a)(y-b) = (d-b)(x-a)`

Here that's

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

`-7y -28 = 10x - 30`

`-28+30 = 10x + 7y`

Answer:
`10x + 7y = 2`

Check:

10(3)+7(-4)=30-28=2, good

10(-4)+7(6)=-40+42=2, good

Answer 2

10x + 7y = 2

Explanation:

Slope = (6 + 4)/(-4 - 3) = -10/7

Equation:

y + 4 = -10/7(x - 3)

7(y + 4) = - 10(x - 3)

7y + 28 = -10x + 30

10x + 7y = 30 - 28

10x + 7y = 2