Respuesta :

semsee45

Answer:

[tex]y\leq \dfrac12x+3[/tex]

Step-by-step explanation:

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

  • Let [tex]\sf (x_1,y_1)=(-6,0)[/tex]
  • Let [tex]\sf (x_2,y_2)=(0,3)[/tex]

[tex]\sf slope=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-3}{-6-0}=\dfrac12[/tex]

point-slope form of linear equation:  [tex]\sf y-y_1=m(x-x_1)[/tex]

[tex]\implies \sf y-0=\dfrac12(x-(-6))[/tex]

[tex]\implies \sf y=\dfrac12x+3[/tex]

Solid line : ≤ or ≥

Dashed line: < or >

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

[tex]\implies \sf y\leq \dfrac12x+3[/tex]
  • (0,3)
  • (2,4)

Slope:-

[tex]\\ \tt\Rrightarrow m=\dfrac{4-3}{2}=1/2[/tex]

Equation of line in point slope form

[tex]\\ \tt\Rrightarrow y-3=1/2x[/tex]

[tex]\\ \tt\Rrightarrow y=1/2x+3[/tex]

Equation of shaded region

[tex]\\ \tt\Rrightarrow y\leqslant 1/2x+3[/tex]

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