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Determine the equation of the line given by the graph.

A) y = 2 3 x − 1

B) y = 3 2 x − 1

C) y = −2 3 x − 1

D) y = −3 2 x − 1

Determine the equation of the line given by the graph A y 2 3 x 1 B y 3 2 x 1 C y 2 3 x 1 D y 3 2 x 1 class=

Respuesta :

This function is increasing, so the slope should be positive.

slope=rise/run=2/3

A) y = (2/3) x − 1 

Answer:

A. [tex]y=\frac{2}{3}x-1[/tex]

Step-by-step explanation:

The given graph belongs to a linear function, because it's a line.

To find its equation, we first need to find the slope of the line using two points and the formula

[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

We are gonna use points (0,-1) and (3,1), because the lines crosses through them. Replacing these points in the formula, we have

[tex]m=\frac{1-(-1)}{3 -0 }=\frac{1+1}{3}\\m=\frac{2}{3}[/tex]

Now, we use one points and the point-slope formula

[tex]y -y_{1} =m(x-x_{1} )\\y-(-1)=\frac{2}{3}(x-0)\\ y+1=\frac{2}{3}x\\y=\frac{2}{3}x-1[/tex]

Therefore, the right answer is A.

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

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