Question

What is the equation of the line between `(5,2)` and `(-1,3)`?

Answer 1

`y=-1/6x+17/6`

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)=(5,2)" and "(x_2,y_2)=(-1,3)`

`rArrm=(3-2)/(-1-5)=1/(-6)=-1/6`

`rArry=-1/6x+blarrcolor(blue)"is the partial equation"`

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

`"using "(5,2)" then"`

`2=-5/6+brArrb=12/6+5/6=17/6`

`rArry=-1/6x+17/6larrcolor(red)"in slope-intercept form"`