Question

How do you write an equation of the line in standard form with m = 4/3 (-2,-6)?

Answer 1

First write the equation in slope-point form
then convert to standard form, to get
`color(white)("XXX")4x-3y=10`

Explanation:

Slope-point form:
`color(white)("XXX")(y-haty)=m(x-hatx)`
`color(white)("XXXXXXXXX")`for a line with slope `m` through the point `(hatx,haty)`

For the given data this becomes
[1]`color(white)("XXX")y+6 =4/3(x+2)`

Standard form for a linear equation is
`color(white)("XXX")Ax+By=C`
`color(white)("XXXXXXXXX")`for `A,B,C in ZZ` and `A>=0`

Simplifying [1]
[2]`color(white)("XXX")3y+18=4x+8`

Subtracting `(3y+8)` from both sides
[3]`color(white)("XXX")10 = 4x-3y`

Reversing the sides to get standard form:
[4]`color(white)("XXX")4x-3y=10`