Question

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

Answer 1

`y=-2x+2`

Explanation:

`color(blue)("Determine the initial structure of the equation")`

Standard form of the equation is`" "y=mx+c"`

The slope (gradient) is given as -2 so we now have

`y=-2x+c`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the value of the constant "c)`

Given that the 'straight' line passes through the point

`" "(x,y)->(color(green)(2),color(red)(-2))`

Substitute in the equation to find the value of c

`color(red)(y)=-2color(green)(x)+c" "->" "color(red)(-2)=-2(color(green)(2))+c`

`color(brown)(" "-2=-4+c)`

Add `color(blue)( 4)` to both sides

`color(brown)(" "-2color(blue)(+4)= -4color(blue)(+4)+c`

`+2=0+c`

`c=2`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Putting it all together")`

`y=-2x+2`