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

Algebra ->  Linear-equations -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

3y-12x=7 Start with the given equation.


3y=7%2B12x Add 12x to both sides.


3y=12x%2B7 Rearrange the terms.


y=%2812x%2B7%29%2F%283%29 Divide both sides by 3 to isolate y.


y=%28%2812%29%2F%283%29%29x%2B%287%29%2F%283%29 Break up the fraction.


y=4x%2B7%2F3 Reduce.



We can see that the equation y=4x%2B7%2F3 has a slope m=4 and a y-intercept b=7%2F3.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=4.


Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=4 and the coordinates of the given point .


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-6=4%28x-0%29 Plug in m=4, x%5B1%5D=0, and y%5B1%5D=6


y-6=4x%2B4%280%29 Distribute


y-6=4x%2B0 Multiply


y=4x%2B0%2B6 Add 6 to both sides.


y=4x%2B6 Combine like terms.


So the equation of the line parallel to 3y-12x=7 that goes through the point is y=4x%2B6.


Here's a graph to visually verify our answer:
Graph of the original equation y=4x%2B7%2F3 (red) and the parallel line y=4x%2B6 (green) through the point .

Answer by oscargut(2103) About Me  (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