Question

Complete the equation of the line through (-8,8) and (1,-10)

Answer 1

`\[y+2x=-8\]`

Explanation:

The equation of a line passing through two given points (x1,y1) and (x2,y2) is given by:

`\[((x-x1))/((x2-x1))=((y-y1))/((y2-y1))\]`

In this case, x1=-8,y1=8,x2=1,y2=-10

Substituting these values in the equation:

`\[((x-(-8)))/((1-(-8)))=((y-8))/((-10-8))\]`

Simplifying,

`\[((x+8))/((1+8))=((y-8))/((-18))\]`

=>
`\[((x+8))/(9)=((y-8))/((-18))\]`

=>
`\[((x+8))/(9)*(-18)=(y-8)\]`

=>
`\[-2x-16=y-8\]`

=>
`\[-8=y+2x\]`