Question

Express `y-4 =-2(x-3)` in general form?

Answer 1

`2x+y-10=0`

Explanation:

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

Here we have an equation of a straight line.

Probably the most common form of the equation of a straight line is the so called, "slope and intercept" form.

Here `y=mx+c`; where `m` is the slope of the line and `c` is the `y-`axis intercept.

However, the most general form of the equation of a straight line is:

`ax + by +c =0`; where `a,b and c` are real constants.

Expanding the RHS of our equation:

`y-4 = -2x+6`

Hence, `2x+y -10=0` is our equation in its most general form, where `(a=2, b=1, c=-10)`

Incidentally, in slope and intercept form, this equation is:

`y=-2x +10`,

so the slope is `-2` and `y-`intercept is `+10` as can be seen by the graph of the general equation below:

graph{2x+y -10=0 [-28.88, 28.85, -14.43, 14.45]}