SOLUTION: L has y-intercept(0,2) and is perpendicular to the line with equation 2x-3y=6. I have a hard time with problems like these. please help

Question 27578: L has y-intercept(0,2) and is perpendicular to the line with equation 2x-3y=6. I have a hard time with problems like these. please help
Found 2 solutions by longjonsilver, yougan aungamuthu:
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
questions like these are straight forward... just need to build it up slowly.

Line L has an equation of the form y=mx+c...we need to find m, the gradient , and c - the y-intercept. The question will give you the info somewhere. You just need to find it :-)

So, first, gradient.
The Q says that L is perpendicular to the other line quoted. Perpendicular means that they are at right angles to each other. Now, the gradients of 2 lines that are perpendicular (call the gradients m and n) multiply to give -1, so we can use this fact to find the gradient of L.

First, what is the gradient of the other line?

2x-3y=6
2x = 3y+6
or 3y+6 = 2x
3y = 2x-6
y = (2/3)x-2

so its gradient is (2/3)

So our gradient, call it m, is -(3/2) which is found from: m*n = -1

--> m*(2/3) = -1
--> m = -(3/2)

So, our equation is y = -(3/2)x + c
Now we need to find the value of c. To do this, we need to know a set of values of (x,y) on the line. We are given this... (0,2)

so, y = -(3/2)x + c becomes
2 = -(3/2)*0 + c
2 = 0 + c
--> c = 2

so, the equation of L is y = -(3/2)x + 2 which is an answer. We can get rid of the fraction, giving 2y = -3x + 4 and then possibly move the x too to give 2y + 3x = 4.

Any of these versions is correct.

Hope that helps

jon.

Answer by yougan aungamuthu(2) (Show Source): You can put this solution on YOUR website!
STEP 1
What is given?
* line L with y-intercept (0,2)
* line with equation 2x-3y=6 but perpendicular to line L
STEP 2
Draw a diagram
STEP 3
To find the equation of any line you need 2 things, namely,
gradient and a point on the line you want to find the equation of.
STEP 4
The point on L is (0,2)
The gradient we get from the line 2x-3y=6 since it is perpendicular
to L. What do we know about perpendicular lines? Yes, the product
of their gradients is -1.
What is the gradient of 2x-3y=6? Write 2x-3y=6 in the y-form i.e
make y subject of the formula. Thus
2x-3y=6
-3y=6-2x
y=-2+(2/3)x
which means the gradient is 2/3.
STEP 5
since the lines are perpendicular, the product of gradients is -1
(gradient L)(2/3)= -1 therefore
gradient L = -3/2
Step 6 using the formula for a straight line y=mx+c
we substitute for m, which is the gradient L = -3/2
and c, which is the y-intercept 2 to get the required
equation of L y = (-3/2)x + 2

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