Question 27578
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.