Question

PLEASE HELP ASAP

4. The equation for line m is y= 1/2x - 5 . Use this information and these descriptions to write an equation for line n, line p, and line r.
(a) Line m and line n have no solutions. Write an equation that can represent line n.
(b) Line m and line p have infinitely many solutions. Write an equation that can represent line p.
(c) Line m and line r have one solution. Write an equation that can represent line r.

Answer 1

(a) Equation of line n is
`y=(1)/(2)x`. (b) Equation of line p is
`y=(1)/(2)x-5`. (c) Equation of line r is
`y=x`.

Step-by-step explanation:

The equation of line m is

`y=(1)/(2)x-5`

It is a slope intercept form of a line, therefore the slope of the line is
`(1)/(2)`.

(a)

Two line have no solution if and only if both lines are parallel. The slope of two parallel lines are same, therefore the slope of the line n is must be
`(1)/(2)`.

The equation for line n is in the form of

`y=(1)/(2)x+c`

Where c can be any real number except -5.

An equation for line n is

`y=(1)/(2)x`

(b)

Two line have infinitely many solutions if and only if both lines are same.

Therefore the equation of line p is same as equation of line m.

`y=(1)/(2)x-5`

(c)

Two line have exactly one solution if and only if both lines intersecting each other at a single point. To lines intersect each other if their slopes are different.

Therefore the slope of line r is not equal to
`(1)/(2)`.

The equation for line r is in the form of

`y=mx+c`

Where c can be any real number and m can be any real number except
`(1)/(2)`.

An equation for line r is

`y=x`