Question

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

Answer 1

Answer:

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

Step-by-step 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 - $y_{1}$   = $\frac{y_{2} - y_{1} }{x_{2} - x_{1}}$  ( x - $x_{1}$  )

i.e.  y - (-4)= $\frac{17 - (-4)}{-10 - 5}$  ( x- 5)

     y + 4 = $\frac{17 + 4}{ -15}$ ( x - 5)

     y + 4 = $\frac{21}{-15}$  ( x - 5 )

     ( y + 4)  =  $\frac{7}{- 5}$ ( 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.