is the correct answer because when each term is divided by 2 in order to see the equation in terms of y, the slope of the equation is , which is the same as the slope in the given equation. Parallel lines have the same slope. 

The equation of a line can be written using the expression  where  is the slope and  is the y-intercept. When lines are parallel to each other, it means that they have the same slope, so . The y-intercept is given in the problem as . This means that the equation would be .

In order to approach this problem, we need to be familiar with the slope-intercept equation of a line, where m is the slope and b is the y-intercept. The line that our line is supposed to be parallel to is . Lines that are parallel have the same slope, m, so the slope of our new line is . Since we don't know the y-intercept yet, for now we'll write our equation as just:

. We can solve for b using the point we know the line passes though, . We can plug in 4 for x and -2 for y to solve for b:

first we'll multiply to get 1:

 now we can subtract 1 from both sides to solve for b:

Now we can just go back to our equation and sub in -3 for b:

Parallel lines have the same slope. So our line should have a slope of 2x. Next we use the point slope formula to find the equation of the line that passes through  and is parallel to .

Point slope formula:

 is the slope of the line parallel to  which passes through .

Parallel lines have the same slope, so the slope of the new line will also have a slope 

Use point-slope form to find the equation of the new line.

Plug in known values and solve.

This problem can be easily solved through using the point-slope formula:

 where  is the slope and  and  signify one of the given points (coordinates).

The problem provides us with two points, so that requirement is fulfilled. We may choose either one when substituting in our values. The only other requirement left is slope. The problem also provides us with this information, but it's not as obviously given. The problem specifies that the line of interest is parallel to . By definition, lines are parallel when they have the same slope. Given that information, if the two lines are parallel, the line of interest will have the same slope as the given equation: . Therefore, we have our required point and the slope. Now we may substitute in all the information and solve for the equation. 

Here, we arbitrarily choose the point .

This problem can be easily solved through using the point-slope formula:

 where  is the slope and  and  signify one of the given points (coordinates).

The problem provides us with two points, so that requirement is fulfilled. We may choose either one when substituting in our values. The only other requirement left is slope. The problem also provides us with this information, but it's not as obviously given. The problem specifies that the line of interest is parallel to a line with a slope of . By definition, lines are parallel when they have the same slope. Given that information, if the two lines are parallel, the line of interest will have the same slope as the given equation:. Therefore, we have our required point and the slope. Now we may substitute in all the information and solve for the equation. 

Here, we arbitrarily choose the point .

This problem can be easily solved through using the point-slope formula:

 where  is the slope and  and  signify one of the given points (coordinates).

The problem provides us with two points, so that requirement is fulfilled. We may choose either one when substituting in our values. The only other requirement left is slope. The problem also provides us with this information, but it's not as obviously given. The problem specifies that the line of interest is parallel to .  By definition, lines are parallel when they have the same slope. Given that information, if the two lines are parallel, the line of interest will have the same slope as the given equation: . Therefore, we have our required point and the slope. Now we may substitute in all the information and solve for the equation. 

Here, we arbitrarily choose the point .

The first thing we need to do is determine the slope of this parallel line. Recall that parallel lines have the same slope, so the slope of this new line must be .

Next, we must determine the -intercept of the line. The equation for a line is given to us by , and here we know three of the four variables in this new line: .

So when we plug in these numbers we get 

Multiply to get:

Subtract  from both sides to get:

Therefore, the equation for the line is:

If f(x) is parallel to g(x) and passes through the point (-4,8), what is the equation of f(x)?

If f(x) is parallel to g(x), then it must have the same slope. 

So,

We also know that f(x) goes through the point (-4,8)... Set up the following:

Where b is our y-intercept, which we need to solve for:

Finally, put it all together: