l has y intercept

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exw9141

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Jan 13, 2006
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L has y intercept (0, -3) and is parallel to the line with equation y = 2/3x=1.

I am supposet to write the equation of the L satisfying the given geometric conditions.

I am totally lost and I understand the slope equation but the satisfying L part has me baffled.

Please help! :(
 
1) "L has y intercept (0, -3) "

2) "is parallel to the line with equation y = 2/3x=1"
L has a slope equal to the slope of any line parallel to it.

Consider that L has equation of the form y = mx + c, where m is its slope and c is the y-ordinate of its y-intercept.
 
answer????

So would I be looking y = 2/3x -4

y - (-3) = 2/3[x-1]

i think i wrote this write according to the school book. online is not much good if you are not a quick learner. huh?
 
Remember, knowing that our line L is parallel to the line y = (2/3)x - 1 only tells us that the slope of L is 2/3. That's all we know L shares in common with y = (2/3)x - 1.

However, we also know that L has a y-intercept of -3.

These two pieces of information are enough for us to determine L's equation.

Compare with
y = mx + c

We have m = 2/3 (you've got this sorted)

and c = -3

So the equation of our line is: y = (2/3)x - 3

Or, if you wish to use the straight-line equation as you have, we know L's slope is 2/3, and also that it passes through (0, -3) - the y-intercept - so plug these into y - y1 = m(x - x1):

y - -3 = (2/3)(x - 0)

Simplify

y + 3 = (2/3)x

ie.

y = (2/3)x - 3
 
Thank You

I feel more comfortable now. Thanks

one more thing and I am done. I have word problems that are asking:
In planning for a new item, a manufacturer assumes that
the number of items produced x and the cost in dollars C of producing these items
are related by a linear equation. Projections are that 100 items will cost $10,000 to
produce and that 300 items will cost $22,000 to produce. Find the equation that
relates C and x.

Do I use the equation: Ax + By = C
 
Try thinking in terms of coordinates.

When x=100, C=10000

and when x=300, C=22000

You could let x be on the x-axis, and C be on the y-axis.

If you plot those two points, you can see that you can form an equation for the line that passes through those two points.

That line is a model linear function of C in terms of x. For instance, you could use the equation of that line to predict what the cost is (C=?) when 200 items are produced (x=200).

As for the actual forming of the equation,

m = slope = rise/run = ?

and you can use the equation y - y1 = m(x - x1) using the coordinates of either of the known points.
 
C=

I am still a little lost, but I will figure it out. You have helped me a lot. Thank You!
 
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