Question

How do you write an equation that contains points (4, -1) and (-2, -13)?

Answer 1

`y=2x-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)=(4,-1)" and "(x_2,y_2)=(-2,-13)`

`rArrm=(-13-(-1))/(-2-4)=(-12)/(-6)=2`

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

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

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

`-1=8+brArrb=-1-8=-9`

`rArry=2x-9larrcolor(red)"is equation of line"`