Question

How do you write the equation in slope intercept form given (0,2):(4,4)?

Answer 1

`y=1/2x+2`

Explanation:

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`"to calculate m use the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(0,2)" and "(x_2,y_2)=(4,4)`

`m=(4-2)/(4-0)=2/4=1/2`

`y=1/2x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute either of the 2 given points into"`
`"the partial equation"`

`"using "(4,4)" then"`

`4=2+brArrb=4-2=2`

`y=1/2x+2larrcolor(red)"in slope-intercept form"`