Question

How do you write an equation in standard form when given slope and point on line (4, 1), m = -1/2?

Answer 1

The equation of the line is `y=-1/2x+3`

Explanation:

Let the equation of line is `y=mx+c or y= -1/2x+c ; (4,1)` is on the line. So `1= -1/2*4 +c or c=3`. Hence the equation of the line is `y=-1/2x+3` [Ans]

Answer 2

`y=-1/2x+3`

Explanation:

We can write the equation in `color(blue)"point-slope form"`

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

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

substitute these values into the equation.

`y-1=-1/2(x-4)`

distribute the bracket and simplify.

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

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

`rArry=-1/2x+3" is equation in standard form"`