Question

50 POINTS FOR CORRECT AWNSER!

Answer 1

• (-1,3)
• (-2,6)

Slope:-

`\\ \tt\Rrightarrow m=(6-3)/(-2+1)=\frac{-3}`

Equation of line in point slope form

`\\ \tt\Rrightarrow y-3=-3(x+1)`

`\\ \tt\Rrightarrow y=-3x`

Equation of the shaded region

`\\ \tt\Rrightarrow y<-3x`

Answer 2

`y < -3x`

Explanation:

Choose 2 points on the line: (0, 0) and (1, -3)

• Let
  `\sf (x_1,y_1)=(0,0)`
• Let
  `\sf (x_2,y_2)=(1,-3)`

`\sf slope=(y_2-y_1)/(x_2-x_1)=(-3-0)/(1-0)=-3`

point-slope form of linear equation:
`\sf y-y_1=m(x-x_1)`

`\implies \sf y-0=-3(x-0)`

`\implies \sf y=-3x`

Solid line : ≤ or ≥

Dashed line: < or >

Therefore as the line is dashed, and the shading is below the line,

`\implies \sf y < -3x`