Question

50 POINTS FOR CORRECT AWNSER

Answer 1

• (-4,-3)
• (8,6)

Slope:-

`\\ \tt\Rrightarrow m=(6+3)/(8+4)=(9)/(12)=(3)/(4)`

Equation of line in point slope form

`\\ \tt\Rrightarrow y+3=3/4(x+4)`

`\\ \tt\Rrightarrow y+3=3/4x+3`

`\\ \tt\Rrightarrow y=3/4x`

equation of shaded region

`\\ \tt\Rrightarrow y\leqslant 3/4x`

Answer 2

`\sf y \leq \frac34x`

Explanation:

Choose 2 points on the line: (0, 0) and (4, 3)

• Let
  `\sf (x_1,y_1)=(0,0)`
• Let
  `\sf (x_2,y_2)=(4,3)`

`\sf slope=(y_2-y_1)/(x_2-x_1)=(3-0)/(4-0)=\frac34`

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

`\implies \sf y-0=\frac34(x-0)`

`\implies \sf y=\frac34x`

Solid line : ≤ or ≥

Dashed line: < or >

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

`\implies \sf y \leq \frac34x`