Question

What is the equation of the line passing through `(-1,5)` and `(14,-3)`?

Answer 1

`y=-8/15x+67/15`

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)=(-1,5)" and "(x_2,y_2)=(14,-3)`

`rArrm=(-3-5)/(14-(-1))=(-8)/15=-8/15`

`rArry=-8/15x+blarrcolor(blue)"is the partial equation"`

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

`"using "(-1,5)" then"`

`5=8/15+brArrb=75/15-8/15=67/15`

`rArry=-8/15x+67/15larrcolor(red)"equation of line"`