SOLUTION: write an equation of the line that passes thru the given point and is parallel to given line. write in slope intercept form. (0,6), 3y-12x=7

Question 166654: write an equation of the line that passes thru the given point and is parallel to given line. write in slope intercept form.
(0,6), 3y-12x=7
Found 2 solutions by jim_thompson5910, oscargut:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation.

Add to 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

Distribute

Multiply

Add 6 to 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 .

Answer by oscargut(2103) (Show Source): You can put this solution on YOUR website!
original line is 3y-12x=7
then this line in slope-intercept form is: y=4x+7/3
parallel lines are: y=4x+b (b real)
if the line passes thru (0,6) then b=6
Answer: y = 4x+6

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