Question

What is the equation for a line that passes through the points (5,-4) and (-10,17

Answer 1

The equation of the line is 7 x +5 y = 15.

Explanation:

Here the given points are ( 5, -4) & ( -10, 17) -

Equation of a line whose points are given such that

(
`x_(1),y_(1)` ) & (
`x_(2), y_(2)` )-

y -
`y_(1)` =
`(y_(2) - y_(1)  )/(x_(2) - x_(1))` ( x -
`x_(1)` )

i.e. y - (-4)=
`(17 - (-4))/(-10 - 5)` ( x- 5)

y + 4 =
`(17 + 4)/( -15)` ( x - 5)

y + 4 =
`(21)/(-15)` ( x - 5 )

( y + 4) =
`(7)/(- 5)` ( x - 5)

5 (y + 4 ) = - 7 (x - 5 )

5 y + 20 = -7 x + 35

7 x + 5 y = 15

Hence the equation of the required line whose passes trough the points ( 5, -4) & ( -10, 17) is 7 x + 5 y = 15.