Final answer:
The equation of line g parallel to line f and passing through the point (-1, -1) is y = Ex + 11. They share the same slope E but have different y-intercepts.
Step-by-step explanation:
The question asks for the equation of line g, which is parallel to line f with the equation y = Ex - 10 and passes through the point (-1, -1). Since line g is parallel to line f, it must have the same slope (represented by E in the equation). Therefore, the slope of line g will also be E. However, the y-intercept of line g will be different because it passes through a different point.
To find the equation of line g, we use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the given point (-1, -1) and the slope E, we get y - (-1) = E(x - (-1)), simplifying to y + 1 = Ex + E. To write this in slope-intercept form (y = mx + b), we isolate y to get y = Ex + (E - 1).
In order to determine the exact value of E, we would need additional information. However, given that E is constant and the fact that (-1, -1) is a point on the line g, we can solve for the y-intercept by setting x to -1 and y to -1 in our equation. This gives us -1 = E(-1) + b, and solving for b will give us the y-intercept for line g. Therefore, the equation of line g will be in the form of y = Ex + b, where b is the y-intercept found by substituting the values of x and y from the point (-1, -1).
So the correct answer is B. y = Ex + 11, because when you substitute x = -1 and y = -1 into the equation y = Ex + b, you get -1 = E(-1) + b which simplifies to b = 11.