Question

50 POINTS FOR CORRECT AWNSER!

Answer 1

• (0,3)
• (2,4)

Slope:-

`\\ \tt\Rrightarrow m=(4-3)/(2)=1/2`

Equation of line in point slope form

`\\ \tt\Rrightarrow y-3=1/2x`

`\\ \tt\Rrightarrow y=1/2x+3`

Equation of shaded region

`\\ \tt\Rrightarrow y\leqslant 1/2x+3`

Answer 2

`y\leq \frac12x+3`

Explanation:

Choose 2 points on the line: (-6, 0) and (0, 3)

• Let
  `\sf (x_1,y_1)=(-6,0)`
• Let
  `\sf (x_2,y_2)=(0,3)`

`\sf slope=(y_2-y_1)/(x_2-x_1)=(0-3)/(-6-0)=\frac12`

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

`\implies \sf y-0=\frac12(x-(-6))`

`\implies \sf y=\frac12x+3`

Solid line : ≤ or ≥

Dashed line: < or >

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

`\implies \sf y\leq \frac12x+3`