Question

How do you write the equation of a line given (-4,6) (-1,-3)?

Answer 1

`y=-3x-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)=(-4,6)" and "(x_2,y_2)=(-1,-3)`

`rArrm=(-3-6)/(-1-(-4))=(-9)/3=-3`

`rArry=-3x+blarrcolor(blue)"is the partial equation"`

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

`"using "(-1,-3)" then"`

`-3=3+brArrb=-3-3=-6`

`rArry=-3x-6larrcolor(red)"is equation of line"`