Question

Find the equation of the line parallel to 4x+3y=12 and passing through (-3,2)

Answer 1

paraalell has same slope
for
ax+by=c
an equatio with same slope is
ax+by=z where a and b remain unchanged and z is a constant

so
4x+3y=12
paralell is
4x+3y=z
find waht z is
(-3,2)
(x,y)
inpus -3 for x and 2 for y
4(-3)+3(2)=z
-12+6=z
-6=z


the equation is
4x+3y=-6
or
y=-4/3x-2

Answer 2

REwriting the first equation in the form y=mx+c
3y=-4x+12
y=
`(-4x)/(3) +4`
Gradient m= -4/3
Since parallel lines have equal gradients, then equation of line 2:

`(y-2)/(x-(-3)) = (-4)/(3)`
y-2=
`(-4)/(3) (x+3)`
y-2=
`(-4)/(3) x-4`
y=
`(-4)/(3) x-2`