SOLUTION: 9. 2x - 4y - 14 = 0 15. y = -x -15 I don't understand how to do Linear's can u please tell me step- by- step.

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Question 150403This question is from textbook Algebra
: 9. 2x - 4y - 14 = 0
15. y = -x -15
I don't understand how to do Linear's can u please tell me step- by- step.This question is from textbook Algebra

Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that you want to graph?

# 9

2x+-+4y+-+14+=+0+ Start with the given equation.


-4y-14=0-2x Subtract 2x from both sides.


-4y=0-2x%2B14 Add 14 to both sides.


-4y=-2x%2B14 Combine like terms on the right side.


y=%28-2x%2B14%29%2F%28-4%29 Divide both sides by -4 to isolate y.


y=%281%2F2%29x-7%2F2 Simplify.




Looking at y=%281%2F2%29x-7%2F2 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=1%2F2 and the y-intercept is b=-7%2F2


Since b=-7%2F2 this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point

drawing%28500%2C500%2C-10%2C10%2C-10%2C10%2C%0D%0A++grid%281%29%2C%0D%0A++blue%28circle%280%2C-7%2F2%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C-7%2F2%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C-7%2F2%2C.15%29%29%0D%0A%29


Now since the slope is comprised of the "rise" over the "run" this means
slope=rise%2Frun

Also, because the slope is 1%2F2, this means:

rise%2Frun=1%2F2


which shows us that the rise is 1 and the run is 2. This means that to go from point to point, we can go up 1 and over 2



So starting at , go up 1 unit
drawing%28500%2C500%2C-10%2C10%2C-10%2C10%2C%0D%0A++grid%281%29%2C%0D%0A++blue%28circle%280%2C-7%2F2%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C-7%2F2%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C-7%2F2%2C.15%29%29%2C%0D%0A++blue%28arc%280%2C-7%2F2%2B%281%2F2%29%2C2%2C1%2C90%2C270%29%29%0D%0A%29

and to the right 2 units to get to the next point
drawing%28500%2C500%2C-10%2C10%2C-10%2C10%2C%0D%0A++grid%281%29%2C%0D%0A++blue%28circle%280%2C-7%2F2%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C-7%2F2%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C-7%2F2%2C.15%29%29%2C%0D%0A++blue%28circle%282%2C-5%2F2%2C.15%2C1.5%29%29%2C%0D%0A++blue%28circle%282%2C-5%2F2%2C.1%2C1.5%29%29%2C%0D%0A++blue%28arc%280%2C-7%2F2%2B%281%2F2%29%2C2%2C1%2C90%2C270%29%29%2C%0D%0A++blue%28arc%28%282%2F2%29%2C-5%2F2%2C2%2C2%2C+180%2C360%29%29%0D%0A%29


Now draw a line through these points to graph y=%281%2F2%29x-7%2F2

drawing%28500%2C500%2C-10%2C10%2C-10%2C10%2C%0D%0A++grid%281%29%2C%0D%0A++graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C%281%2F2%29x-7%2F2%29%2C%0D%0A++blue%28circle%280%2C-7%2F2%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C-7%2F2%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C-7%2F2%2C.15%29%29%2C%0D%0A++blue%28circle%282%2C-5%2F2%2C.15%2C1.5%29%29%2C%0D%0A++blue%28circle%282%2C-5%2F2%2C.1%2C1.5%29%29%2C%0D%0A++blue%28arc%280%2C-7%2F2%2B%281%2F2%29%2C2%2C1%2C90%2C270%29%29%2C%0D%0A++blue%28arc%28%282%2F2%29%2C-5%2F2%2C2%2C2%2C+180%2C360%29%29%0D%0A%29 So this is the graph of y=%281%2F2%29x-7%2F2 through the points and





# 15





Looking at y=-x-15 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=-1 and the y-intercept is b=-15


Since b=-15 this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point

drawing%28500%2C500%2C-10%2C10%2C-18%2C2%2C%0D%0A++grid%281%29%2C%0D%0A++blue%28circle%280%2C-15%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C-15%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C-15%2C.15%29%29%0D%0A%29


Now since the slope is comprised of the "rise" over the "run" this means
slope=rise%2Frun

Also, because the slope is -1, this means:

rise%2Frun=-1%2F1


which shows us that the rise is -1 and the run is 1. This means that to go from point to point, we can go down 1 and over 1



So starting at , go down 1 unit
drawing%28500%2C500%2C-10%2C10%2C-18%2C2%2C%0D%0A++grid%281%29%2C%0D%0A++blue%28circle%280%2C-15%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C-15%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C-15%2C.15%29%29%2C%0D%0A++blue%28arc%280%2C-15%2B%28-1%2F2%29%2C2%2C-1%2C90%2C270%29%29%0D%0A%29

and to the right 1 unit to get to the next point
drawing%28500%2C500%2C-10%2C10%2C-18%2C2%2C%0D%0A++grid%281%29%2C%0D%0A++blue%28circle%280%2C-15%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C-15%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C-15%2C.15%29%29%2C%0D%0A++blue%28circle%281%2C-16%2C.15%2C1.5%29%29%2C%0D%0A++blue%28circle%281%2C-16%2C.1%2C1.5%29%29%2C%0D%0A++blue%28arc%280%2C-15%2B%28-1%2F2%29%2C2%2C-1%2C90%2C270%29%29%2C%0D%0A++blue%28arc%28%281%2F2%29%2C-16%2C1%2C2%2C+0%2C180%29%29%0D%0A%29


Now draw a line through these points to graph y=-x-15

drawing%28500%2C500%2C-10%2C10%2C-18%2C2%2C%0D%0A++grid%281%29%2C%0D%0A++graph%28500%2C500%2C-10%2C10%2C-18%2C2%2C-x-15%29%2C%0D%0A++blue%28circle%280%2C-15%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C-15%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C-15%2C.15%29%29%2C%0D%0A++blue%28circle%281%2C-16%2C.15%2C1.5%29%29%2C%0D%0A++blue%28circle%281%2C-16%2C.1%2C1.5%29%29%2C%0D%0A++blue%28arc%280%2C-15%2B%28-1%2F2%29%2C2%2C-1%2C90%2C270%29%29%2C%0D%0A++blue%28arc%28%281%2F2%29%2C-16%2C1%2C2%2C+0%2C180%29%29%0D%0A%29 So this is the graph of y=-x-15 through the points and

Answer by stanbon(48545) About Me  (Show Source):
You can put this solution on YOUR website!
9. 2x - 4y - 14 = 0
Divide thru by 2 to get:
x -2y - 7 = 0
solve for "y":
Add 2y to both sides to get:
2y = x - 7
Divide thru by 2 to get:
y = (1/2)x - (7/2)
If x = 0, y = -7/2
If x = 1, y = -3
-------
Plot those two points and draw a line thru them.
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%281%2F2%29x+-%287%2F2%29%29
========================
15. y = -x -15
If x = 0, y=-15
If x = 1, y = -16
Plot those two points and draw a line thru them
-----------
graph%28400%2C300%2C-20%2C20%2C-10%2C10%2C+-x-15%29
==============================
Cheers,
Stan H.