Respuesta :

semsee45

Answer:

[tex]\sf y \leq \dfrac34x[/tex]

Step-by-step explanation:

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

  • Let [tex]\sf (x_1,y_1)=(0,0)[/tex]
  • Let [tex]\sf (x_2,y_2)=(4,3)[/tex]

[tex]\sf slope=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{3-0}{4-0}=\dfrac34[/tex]

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

[tex]\implies \sf y-0=\dfrac34(x-0)[/tex]

[tex]\implies \sf y=\dfrac34x[/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 \dfrac34x[/tex]
  • (-4,-3)
  • (8,6)

Slope:-

[tex]\\ \tt\Rrightarrow m=\dfrac{6+3}{8+4}=\dfrac{9}{12}=\dfrac{3}{4}[/tex]

Equation of line in point slope form

[tex]\\ \tt\Rrightarrow y+3=3/4(x+4)[/tex]

[tex]\\ \tt\Rrightarrow y+3=3/4x+3[/tex]

[tex]\\ \tt\Rrightarrow y=3/4x[/tex]

equation of shaded region

[tex]\\ \tt\Rrightarrow y\leqslant 3/4x[/tex]

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