SOLUTION: x-2y=4 2x-4y=-12 graph both linear eqations in the same rectangular coordination system.Decide if the lines are parallel,perpendicular or neither

Algebra ->  Graphs -> SOLUTION: x-2y=4 2x-4y=-12 graph both linear eqations in the same rectangular coordination system.Decide if the lines are parallel,perpendicular or neither      Log On


   

Question 217241: x-2y=4
2x-4y=-12
graph both linear eqations in the same rectangular coordination system.Decide if the lines are parallel,perpendicular or neither
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
x-2y=4
2x-4y=-12

Step 1. Let's put the above equations in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b).

Step 2. Let's start with x-2y=4

Add 2y-4 to both sides of the equation

x-2y%2B2y-4=4%2B2y-4

x-4=2y

Divide 2 to both sides of the equation

x%2F2-4%2F2=2y%2F2

x%2F2-2=y or y=x%2F2-2

Step 3. In Step 2, the slope m=1/2 and the y-intercept b=-2.

Step 4. Next, let's look at 2x-4y=-12 and put it in slope-intercept form.

Add 4y+12 to both sides of the equation

2x-4y%2B4y%2B12=-12%2B4y%2B12

2x%2B12=4y

Divide 4 to both sides of the equation.

2x%2F4%2B12%2F4=4y%2F4

x%2F2%2B3=y or y=x%2F2%2B3

Step 4. In Step 3, the slope m=1/2 and the y-intercept b=3.

Step 5. ANSWER: Based on Steps 2 and 4, the slopes are both equal to 1/2 which means the lines are parallel. This will be evident on the graph below in Step 6.

y=x%2F2-2
y=x%2F2%2B3

Step 6. ANSWER: Now, graph the equations that is now in slope-intercept form (note on the graph the y-intercepts at x=0 to know which equation is which)

graph%28400%2C400%2C-10%2C+10%2C+-10%2C+10%2C+x%2F2-2%2Cx%2F2%2B3%29

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J