Let us find the slope of the line : x+ 4y = 6
we can write it as 4y = -x +6
y = -(1/4) x + ( 6/4)
slope of the line y= mx + b is m
so here slope = m = -1/4
because we have to find a paraller line so the slope for required line would be same : -1/4
equation of the line having slope m and passing through x1 y1 is :
Y= m( X-x1) + y1
let's plug m= -1/4 x1= -8 and y1 = 5
Y= (-1/4) ( X- -8) + 5
Y= ( -1/4) ( x+8) + 5
Y= (-1/4)( X ) + (-1/4)( 8) + 5
Y= (-1/4) x + 3
Let us now work on second part :
given line is : 2x- 3y = 12
let's write it -3y = -2x +12
y= (-2/-3) x + ( 12/ -3)
Y= ( 2/3) x - 4
slope of this line is 2/3
the required line is perpendicular to it
so the slope of required line = negative resiprocal of this slope =
(-1/ slope of this line ) = -1/( 2/3) = -3/2
Equation of line with slope m= -3/2 and passing through x1= 2 and y1 = 6 is :
Y= m( X-x1) + y1
Y= ( -3/2) ( X- 2) + 6
Y= (-3/2) X - 2(-3/2) + 6
Y= ( -3/2 ) X + 9
Answer : for part 1 : Y= ( 2/3) x - 4
Answer for part 2 : Y= ( -3/2 ) X + 9
