write the equation of this line in slope - intercept form.

Explanation:

Step1: Identify two points on the line

We can see the line passes through (0, - 1) and (2,0).

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,-1)$ and $(x_2,y_2)=(2,0)$. Then $m=\frac{0 - (-1)}{2 - 0}=\frac{1}{2}$.

Step3: Identify the y - intercept $b$

The y - intercept is the y - value when $x = 0$. From the point (0, - 1), $b=-1$.

Step4: Write the equation in slope - intercept form

The slope - intercept form is $y=mx + b$. Substituting $m=\frac{1}{2}$ and $b = - 1$, we get $y=\frac{1}{2}x-1$.

Answer:

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