Question

Determine the equation of the line given by the graph.

Answer 1

Answer:

A. $y=\frac{2}{3}x-1$

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

$m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }$

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

$m=\frac{1-(-1)}{3 -0 }=\frac{1+1}{3}\\m=\frac{2}{3}$

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

$y -y_{1} =m(x-x_{1} )\\y-(-1)=\frac{2}{3}(x-0)\\ y+1=\frac{2}{3}x\\y=\frac{2}{3}x-1$

Therefore, the right answer is A.

$y=\frac{2}{3}x-1$

Answer 2

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

slope=rise/run=2/3

A) y = (2/3) x − 1