SOLUTION: There Is Two Problems First one The graph of which equation is Straight line parallel to the graph of Y=2x? And Second one is An equation Of the line that Contains the orig

Question 118103: There Is Two Problems First one
The graph of which equation is Straight line parallel to the graph of Y=2x?
And Second one is
An equation Of the line that Contains the origin and the Point (1,2)
Can U plz Send me answer to This Question
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
#1

Anything parallel to will have a slope of 2. So just add any number (I'm going to add 2) to to get

Notice if we graph and we can see that the two lines are parallel. So this visually verifies our answer.

Graph of (red) and (green)

#2

Remember the origin is the point (0,0)

First lets find the slope through the points (,) and (,)

Start with the slope formula (note:

is the first point (,) and

is the second point (,))

Plug in ,,, (these are the coordinates of given points)

Subtract the terms in the numerator to get . Subtract the terms in the denominator to get

Reduce

So the slope is

------------------------------------------------

Now let's use the point-slope formula to find the equation of the line:

------Point-Slope Formula------
where is the slope, and

is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

Plug in , , and (these values are given)

Distribute

Multiply and to get .

Add to both sides to isolate y

Combine like terms and to get
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Answer:

So the equation of the line which goes through the points (,) and (,) is:

The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is

Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver )

Graph of through the points (,) and (,)

Notice how the two points lie on the line. This graphically verifies our answer.
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