Question

How do you write the standard form of a line given (-2, 4) and has a slope of 1/2?

Answer 1

`y=x/2+5`

Explanation:

`m:"slope of line"`
`P:(x,y)"any point of line"`

`"the standard line equation is "y-y_1=m(x-x_1)`

`"given " m=1/2" ; "P(-2,4)" ; "y_1=4" ; "x_1=-2`

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

`y-4=x/2+1`

`y=x/2+1+4`

`y=x/2+5`

Answer 2

`y=1/2x+5`

Explanation:

The equation of a line in `color(blue)"point-slope form"` 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)=(-2,4)`

substitute these values into the equation.

`rArry-4=1/2(x+2)`

distribute the bracket and collect 'like terms'

`y-4=1/2x+1rArry=1/2x+5" is the equation"`