The line passes through the fixed point and a variable point

MATHEMATICS · Multi-part · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane

Problem

The line

L

passes through the fixed point

(2,5)

and a variable point

(a,7a-1)

, where

a

is a real parameter. (i) Obtain the equation of

L

in terms of the parameter

a

using the two given points. (ii) Determine the value(s) of

a

for which

L

is perpendicular to the line

3x + 4y = 6

. (iii) For the value of

a

found in part (ii), express the equation of

L

in slope–intercept form and state both its slope and

y

-intercept.