Question

What is the equation of the line passing through `(-2,13)` and `(0,-2)`?

Answer 1

`y=-15/2x-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)=(-2,13)" and "(x_2,y_2)=(0,-2)`

`rArrm=(-2-13)/(0-(-2))=(-15)/2=-15/2`

`rArry=-15/2x+blarrcolor(blue)"is the partial equation"`

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

`"using "(0,-2)" then"`

`-2=0+brArrb=-2`

`rArry=-15/2x-2larrcolor(red)"is the equation of the line"`