Question

How do you write the equation of the line given (8, -3) and (-2, 2)?

Answer 1

`y=-1/2x+1`

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)=(8,-3)" and "(x_2,y_2)=(-2,2)`

`rArrm=(2-(-3))/(-2-8)=5/(-10)=-1/2`

`rArry=-1/2x+blarrcolor(blue)"is the partial equation"`

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

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

`2=1+brArrb=2-1=1`

`rArry=-1/2x+1larrcolor(red)"is the equation of the line"`