Question

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

Answer 1

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

slope=rise/run=2/3

A) y = (2/3) x − 1

Answer 2

A.
`y=(2)/(3)x-1`

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

`m=(y_(2)-y_(1) )/(x_(2) -x_(1) )`

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

`m=(1-(-1))/(3 -0 )=(1+1)/(3)\\m=(2)/(3)`

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

`y -y_(1) =m(x-x_(1) )\\y-(-1)=(2)/(3)(x-0)\\ y+1=(2)/(3)x\\y=(2)/(3)x-1`

Therefore, the right answer is A.

`y=(2)/(3)x-1`