Mathematics

Problem

A line

L_1

is represented by

4x + 5y = 40

. Another line

L_2

has slope

m

and

y

-intercept

-1

. The two lines are observed to meet exactly at a point on the

x

-axis. a. (i) Write the equation of

L_2

in standard form in terms of

m

. b. (ii) Determine the value of

m

so that the point of intersection of

L_1

and

L_2

lies on the

x

-axis. c. (iii) Using the value of

m

, find the coordinates of the point of intersection. d. (iv) Verify whether the pair of equations obtained is consistent and independent.