The equation of the line in the image is y = 3x. Option A is the correct choice.
We can see from the graph that the line passes through the point (1, -3). We can use this point to find the slope of the line.
The slope of a line is calculated using the following formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
Using the point (1, -3) and the origin (0, 0), we can calculate the slope of the line as follows:
m = (-3 - 0) / (1 - 0) = -3
We now know that the slope of the line is -3 and that it passes through the point (1, -3). We can use this information to write the equation of the line in slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept.
Substituting -3 for m and (1, -3) for (x, y), we get the following equation:
y = (-3)x + b
To solve for b, we can substitute the values of x and y from the point (1, -3) into the equation:
-3 = (-3)(1) + b
-3 = -3 + b
b = -3 + 3
b = 0
Therefore, the equation of the line is y = -3x. So, Option A is the correct choice.