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
( [tex]x_{1},y_{1}[/tex] ) & ( [tex]x_{2}, y_{2}[/tex] )-
y - [tex]y_{1}[/tex] = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1}}[/tex] ( x - [tex]x_{1}[/tex] )
i.e. y - (-4)= [tex]\frac{17 - (-4)}{-10 - 5}[/tex] ( x- 5)
y + 4 = [tex]\frac{17 + 4}{ -15}[/tex] ( x - 5)
y + 4 = [tex]\frac{21}{-15}[/tex] ( x - 5 )
( y + 4) = [tex]\frac{7}{- 5}[/tex] ( 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.
