Respuesta :

Answer:

[tex]y\geq 2x+3[/tex]

Step-by-step explanation:

the gradient of a line is found by using the formula [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1} }[/tex]

so we get [tex]\frac{5-3}{1-0}=\frac{2}{1} =2[/tex]

the y-intercept is where the line crosses the y-axis which is simply 3

so the equation of this line is [tex]y=2x+3[/tex] in the form [tex]y=mx+c[/tex]

but the question is asking for an inequality, specifically above the line so we get [tex]y\geq 2x+3[/tex]
  • (0,3)
  • (-3,-3)

Slope:-

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

Equation of line in point slope form

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

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

Put (0,0)

  • 2(0)+3=3>0

Hence the inequality is

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

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