Part a:1 .P and Q are the points of intersection of the line y/2 + x/3= 1 with the x and y axes repectively. The gradient of QR is 1/2, where R is the point with x-coordinate 2a,a>0.

a. Find the y-coordinate of R in terms of a

b.Find the value of a if the gradient of PR is -2

P(3,0), Q(0,2), R(2a,?)

If we find the rule for the line connecting points Q and R, we can then substitute 2a into that equation to find y in terms of a.

y intercept is 2 and gradient is 1/2, equation between Q and R is

so y coordinate or R in terms of a is

Part b:

Equation of line R and P has gradient of -2 and x intercept at (3,0)

Finding the equation between the 2 points..

notice R is the intersection between the 2 lines with equations:

and

Simply let y=y in those 2 equations to find x coordinate of the intersection which is 2a.

multiply everything by 2 (so x is no longer a fraction)

get x by itself

we were told to find a: now