Solution:

We are tasked with finding the equation of a line $G$ that passes through the point $(7, 11)$ and is parallel to the line $y = 4(3x + 2)$.

Step 1: Simplify the given equation of the parallel line

The equation of the given line is: $y = 4(3x + 2)$ Simplify it: $y = 12x + 8$ Thus, the slope ($m$) of this line is $12$.

Since line $G$ is parallel, it will have the same slope: $m = 12$

Step 2: Use the point-slope form of the line

The point-slope form is: $y - y_1 = m(x - x_1)$ Substitute $m = 12$, $(x_1, y_1) = (7, 11)$: $y - 11 = 12(x - 7)$

Step 3: Simplify the equation

Expand and simplify: $y - 11 = 12x - 84$ $y = 12x - 84 + 11$ $y = 12x - 73$

Final Answer:

The equation of line $G$ is: $y = 12x - 73$

Would you like further details or have any questions?

Related Questions:

1. How do you find the slope of a line given two points on the line?
2. What is the difference between parallel and perpendicular slopes?
3. How do you convert a point-slope form equation to slope-intercept form?
4. What is the geometric significance of the $y$-intercept in a line equation?
5. How can you verify if two lines are parallel or not?

Tip:

For parallel lines, remember that their slopes are always identical, but their $y$-intercepts will differ unless they overlap.