SOLUTION: Topic : Co-ordinate Geometry (Q) A line passes through the points with co-ordinates (k,2k-3) and (2-k,k-2), where k is a constant. (a) show that the gradient of the line

Algebra ->  Coordinate-system -> SOLUTION: Topic : Co-ordinate Geometry (Q) A line passes through the points with co-ordinates (k,2k-3) and (2-k,k-2), where k is a constant. (a) show that the gradient of the line       Log On


   

Question 565991: Topic : Co-ordinate Geometry
(Q) A line passes through the points with co-ordinates (k,2k-3) and (2-k,k-2),
where k is a constant.
(a) show that the gradient of the line is 1/2 ?
(b) find, in terms of k, an equation of the line ?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
(k,2k-3) and (2-k,k-2),
Slope m = (y2-y1)/(x2-x1)
m=%28%28k-2%29-%282k-3%29%29%2F%28%282-k%29-k%29%29

m= %28k-2-2k%2B3%29%2F%282-2k%29
m=%28-k%2B1%29%2F%282%281-k%29%29

m= %28%281-k%29%29%2F%282%281-k%29%29
m= 1/2

slope = 1/2 & point ( (k,(2k-3))

2k-3= (1/2)*k +b
2k-3-(1/2)k=b
multiply equation by 2
4k-6-k=2b
(3k-6)=2b
3(k-2)=2b
3(k-3)/2 =b
Frame the equation
y = (1/2) x +3(k-2)/2