SOLUTION: Write an equation of the line containing the given point and parallel to the given line. (4,-4), 2x-7y=3 The equation of the line is y=? Simplify the answer. Can anyone help me

Question 243547: Write an equation of the line containing the given point and parallel to the given line.
(4,-4), 2x-7y=3
The equation of the line is y=?
Simplify the answer.
Can anyone help me on this one it really has me stumped. Thanks
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation.

Subtract from both sides.

Rearrange the terms.

Divide both sides by to isolate y.

Break up the fraction.

Reduce.

We can see that the equation has a slope and a y-intercept .

Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is .
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope and the coordinates of the given point

.

Start with the point slope formula

Plug in , , and

Rewrite as

Distribute

Multiply

Subtract 4 from both sides.

Combine like terms.

So the equation of the line parallel to that goes through the point

is .

Here's a graph to visually verify our answer:

Graph of the original equation (red) and the parallel line (green) through the point

.

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