Answer:
y = 12x - 73
Explanation:
Pre-Solving
We are given the line y=4(3x+2).
We want to find the equation of line G, which contains the point (7,11), and is parallel to y=4(3x+2) in the form y=mx+c. m is the slope, and c is the value of y at the y-intercept.
Parallel lines have the same slopes. So, we should start by finding the slope of y=4(3x+2).
Solving
We can do the distributive property to distribute the 4 to both terms on the right side.
y=4(3x+2) => y=12x + 8
Notice how this equation is written in the form y=mx+c. As 12 is written in the place where m is, the slope of this line is 12.
It is also the slope of line G.
We can replace m in y=mx+c with 12 for line G. We'll get:
y=12x + c
Now, we need to find c.
We can use the point (7,11) to help us find c.
Substitute 7 for x and 11 for y.
11 = 12(7) + c
Multiply.
11 = 84 + c
Subtract 84 from both sides
-73 = c
Substitute -73 as c.
y = 12x - 73