Respuesta :

Option B:

The equation of the line given is [tex]y=\frac{1}{3} x+2[/tex].

Solution:

Take any two points on the line of the graph.

Let the points be (0, 2) and (3, 3).

Slope of the line:

[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]$m=\frac{3-2}{3-0}[/tex]

[tex]$m=\frac{1}{3}[/tex]

Using point-slope formula,

[tex]y-y_1=m(x-x_1)[/tex]

[tex]$y-2=\frac{1}{3} (x-0)[/tex]

[tex]$y-2=\frac{1}{3} x-0[/tex]

Add 2 on both sides of the equation.

[tex]$y=\frac{1}{3} x+2[/tex]

The equation of the line given is [tex]y=\frac{1}{3} x+2[/tex].

Hence Option B is the correct answer.

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