Question

What is the equation of the line passing through `(1,4)` and `(-8,2)`?

Answer 1

`y=2/9x+34/9`

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)=(1,4)" and "(x_2,y_2)=(-8,2)`

`rArrm=(2-4)/(-8-1)=(-2)/(-9)=2/9`

`rArry=2/9x+blarrcolor(blue)"is the partial equation"`

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

`"using "(1,4)" then"`

`4=2/9+brArrb=36/9-2/9=34/9`

`rArry=2/9x+34/9larrcolor(red)"is the equation of the line"`