Question

What is the slope intercept form of the line passing through `(1,5)` with a slope of `-1/2`?

Answer 1

`y=-1/2x+11/2`

Explanation:

Standardised slope intercept form: `" "y=mx+c`
Where `m` is the gradient.

Given point`->(x,y)=(1,5)` so we have related values for `x and y`

Given gradient `->-1/2`

So our standardised form become`" "y=-1/2x+c`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We are given that when `y=5" " x=1" "` so by substitution we have:

`" "color(brown)(y=-1/2x+c )color(blue)(" "->" "5=-1/2(1)+c)`

Add `1/2` to both sides

`=> 5+1/2=-1/2+1/2+c`

`=>11/2=0+c`

`=> c= 11/2`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Thus`" "color(brown)(y=mx+c)color(blue)(" "->" "y=-1/2x+11/2`