Graphing Linear Equations?

Question

i'm having a lot of issues solving these three equations, if anyone can help me, please do!
i also need to graph them.
any help is REALLY appreciated. :[

1. 2x – 2y = 6 by graphing 3 points.

2. y equals the absolute value of the quantity x plus 4 by graphing 5 points.

3. y equals the absolute value of the quantity negative one-half x minus 3 by graphing 5 points.

Answer 1

1. Just pick any value of x, solve for y, and use those as an ordered pair.



Let x = 4

2(4) - 2y = 6

8 - 2y = 6

2 = 2y

y = 1



Ordered pair (4,1)



Let x = 6

2(6) - 2y = 6

12 - 2y = 6

2y = 6

y=3



Ordered pair (6,3)



Let x = -5

2(-5) - 2y = 6

-10 - 2y = 6

2y = -16

y=-8



Ordered pair (-5, -8)



So your three points are (4,1), (6,3), (-5,-8)



Graph them and draw your line



2. y = |x+4|



The best way to graph inequalities is to start at x = 0



y = |0+4|

y=4



Ordered pair (0,4)



Then y=0



0=|x+4|

x=-4



Ordered pair (-4,0)



So your y intercept is at x = 4, and your x intercept is at y = -4



Now solve for 3 more points:



Let x = 2



y = |2+4|

y = 6



Ordered pair (2,6)



Let x = -5



y=|-5+4|

y=|-1|

y=1



Ordered pair (-5,1)



Let x = -2



y = |-2+4|

y = 2



Ordered pair (-2, 2)



Graph them, and draw the line. Remember that all functions are drawn from one side to the other. Also remember than an absolute value must have positive solutions. In this case, y will always be positive, but x can be negative, because it's within the absolute value.





3. y = |((-1/2)x) - 3|



Do the same thing you did for number 2, and remember that y will always be positive. I would suggest finding your x and y intercepts first.



Hope this helps.

Answer 2

I'm assuming you're just doing straight lines on basic co-ordinate graphs here, because you didn't provide us with much detail regarding the nature of the questions.



The equation for any straight line is Y=MX+C.

Where M is the gradient and C is the Y intercept.



First re-arrange the equations into the form Y=MX+C.

Then you just need to pick a point on the X axis and substitute it into the equation. Now you can use the equation to figure out the value of Y for that X point.



I think the questions 2 + 3 are exactly the same but they have been expressed in words instead of number values. They shouldn't be to hard to figure out. Just think about it.



Hope this helps.

Answer 3

1. Solve this for y. Any two (or three) points will be fine (two points determine a line).



2. Choose x=0, 2 positive values and 2 negative values.



3. This is centered around x=-6. Use that point, two points larger and 2 points smaller.