write the equation of the line in fully simplified slope-intercept form.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the points ((0, 0)) and ((1, 2)) (we can also use other points, but these are easy to identify).

Step2: Calculate the slope ((m))

The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}). Using the points ((x_1,y_1)=(0,0)) and ((x_2,y_2)=(1,2)), we have: (m=\frac{2 - 0}{1 - 0}=\frac{2}{1} = 2)

Step3: Determine the y - intercept ((b))

The slope - intercept form of a line is (y=mx + b), where (b) is the y - intercept (the value of (y) when (x = 0)). Since the line passes through ((0,0)), when (x = 0), (y=0). Substituting (x = 0), (y = 0) and (m = 2) into (y=mx + b), we get (0=2(0)+b), so (b = 0).

Step4: Write the equation in slope - intercept form

Substitute (m = 2) and (b = 0) into (y=mx + b). We get (y=2x+0), which simplifies to (y = 2x).

Answer:

(y = 2x)