SOLUTION: find the equation of the line through the points (-2,4) parallel to the line 2x+7y=9 i tried solving for "y" but was not really sure if i was doing it right or what to do aft

Algebra ->  Linear-equations -> SOLUTION: find the equation of the line through the points (-2,4) parallel to the line 2x+7y=9 i tried solving for "y" but was not really sure if i was doing it right or what to do aft      Log On


   

Question 156957: find the equation of the line through the points (-2,4) parallel to the line
2x+7y=9
i tried solving for "y" but was not really sure if i was doing it right
or what to do after
-a/b=-2/7
Found 2 solutions by jim_thompson5910, gonzo:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%2B7y=9 Start with the given equation.


7y=9-2x Subtract 2x from both sides.


7y=-2x%2B9 Rearrange the terms.


y=%28-2x%2B9%29%2F%287%29 Divide both sides by 7 to isolate y.


y=%28%28-2%29%2F%287%29%29x%2B%289%29%2F%287%29 Break up the fraction.


y=-%282%2F7%29x%2B9%2F7 Reduce.


We can see that the equation y=-%282%2F7%29x%2B9%2F7 has a slope m=-2%2F7 and a y-intercept b=9%2F7.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=-2%2F7.
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=-2%2F7 and the coordinates of the given point .


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


y-4=%28-2%2F7%29%28x--2%29 Plug in m=-2%2F7, x%5B1%5D=-2, and y%5B1%5D=4


y-4=%28-2%2F7%29%28x%2B2%29 Rewrite x--2 as x%2B2


y-4=%28-2%2F7%29x%2B%28-2%2F7%29%282%29 Distribute


y-4=%28-2%2F7%29x-4%2F7 Multiply


y=%28-2%2F7%29x-4%2F7%2B4 Add 4 to both sides.


y=%28-2%2F7%29x%2B24%2F7 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line parallel to 2x%2B7y=9 that goes through the point is y=%28-2%2F7%29x%2B24%2F7.


Here's a graph to visually verify our answer:
Graph of the original equation y=-%282%2F7%29x%2B9%2F7 (red) and the parallel line y=%28-2%2F7%29x%2B24%2F7 (green) through the point .

Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
parallel line = 2x + 7y = 9.
translate to y = mx+b to get slope.
could also plot a couple of points to get the slope taking (y2-y1)/(x2-x1)
7y = -2x + 9
y = -2x/7 + 9/7
slope is -2/7 so part of the equation is y = -2/7x because parallel lines have the same slope.
to pass through (-2,4), when x = -2, y must be = to 4.
when x = -2, -2/7x = -2/7*-2 = 4/7.
4/7 plus 24/7 = 4, so we have to add 24/7 to the equation.
equation becomes y = (-2/7)x + (24/7).
can multiply both sides by 7 to get 7y = -2x + 24
that should be it.
graphing the equation shows it to be:
graph%28800%2C200%2C-10%2C20%2C-5%2C%2B5%2C%28-2x%2B24%29%2F7%29
plotting some points shows them to be:
x,y
-10,(44/7)
-2,4
0,(24/7)
+2,(20/7)
+10,(4/7)
y intercept is when x = 12 (12,0).