Question

How do you write the equation in standard form given m = -1/2 and (4,6)?

Answer 1

`x+2y-16=0`

Explanation:

The equation of a line in `color(blue)"standard form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(ax+by+c=0)color(white)(2/2)|)))`
where a is a positive integer and b, c are integers.

Begin by expressing the equation in `color(blue)"point-slope form"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))`
where m represents the slope and `(x_1,y_1)" is a point on the line"`

`"here "m=-1/2" and " (x_1,y_1)=(4,6)`

Substituting these values into the equation.

`y-6=-1/2(x-4)larrcolor(red)"point-slope form"`

distributing, simplifying and rearranging.

`y-6=-1/2x+2`

`rArr1/2x+y-8=0`

coefficient of x, that is a must be an integer.

multiplying through by 2

`rArrx+2y-16=0larrcolor(red)" in standard form"`