Mathematics

Problem

Let the two lines

2x - 3y + 7 = 0

and

x + y - 5 = 0

intersect at the point

P

. A third line

L

passes through

P

and makes an angle of

135^{\circ}

with the positive

x

–axis. a. (i) Determine the coordinates of

P

. b. (ii) Find the equation of line

L

in slope–intercept form. c. (iii) Obtain the point where

L

meets the

y

–axis. d. (iv) Compute the area of the triangle enclosed by

L

and the coordinate axes.