Question

What is the equation of the line passing through `(18,23), (12,8)`?

Answer 1

`y=5/2x-22`

Explanation:

`"the equation of a line in "color(blue)"point-slope 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)=(18,23)" and "(x_2,y_2)=(12,8)`

`rArrm=(8-23)/(12-18)=(-15)/(-6)=5/2`

`rArry=5/2x+blarrcolor(blue)"is the partial equation"`

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

`"using "(12,8)" then"`

`8=30+brArrb=8-30=-22`

`rArry=5/2x-22larrcolor(red)"is the equation"`