Mathematics

Problem

Line

L_1

passes through the point

P(2,-3)

and has a slope of

4

. Another line

L_2

is parallel to

L_1

and passes through the point

Q(-1,5)

. a. (i) Find the equations of

L_1

and

L_2

in the form

y = mx + c

. b. (ii) Verify that the two lines are parallel. c. (iii) Determine the

x

-coordinates of the points where each line intersects the horizontal line

y = 1

. d. (iv) Hence, find the distance between these two intersection points on the line

y = 1