Question

find the equation of the line through (-5, 7) with slope -6? ​

Answer 1

Equation of line passing through point (a,b) and has slope m :-

$\underline{\boxed{ \rm \large \: y - b = (x - a)m}}$

Now , we will find equation of the line through (-5, 7) with slope -6.

Now put :-

a = -5

b = 7

m = -6

$\rm \longrightarrow \: y - 7 = (x + 5)( - 6) \\ \\ \\ \rm \longrightarrow \: y - 7 = - 6x - 30\\ \\ \\ \rm \longrightarrow \: y + 6x- 7 = - 30\\ \\ \\ \rm \longrightarrow \: y + 6x = 7- 30\\ \\ \\ \rm \longrightarrow \: y + 6x = -2 3\\ \\ \\ \rm \longrightarrow \: y + 6x +2 3= 0$

Answer :

Equation of the line through (-5, 7) with slope -6 :-

y + 6x + 23 = 0

Answer 2

Answer:

Given :-

(-5, 7) with slope -6?

To Find :-

Equation

Solution :-

$\large \sf \: y - b =(x - a) m$

a = -5

b = 7

m = -6

⟶y−7=(x+5)(−6)

⟶y - 7 =−6x −30

⟶y + 6x −7 = −30

⟶y+ 6x =7 - 30

⟶y + 6x= −23

⟶ y+ 6x+ 23=0

Equation :-

$\bf \huge \: y + 6x + 23 = 0$