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

Answer:

(a) Equation of line n is $y=\frac{1}{2}x$. (b)  Equation of line p is $y=\frac{1}{2}x-5$. (c)  Equation of line r is $y=x$.

Explanation:

The equation of line m is

$y=\frac{1}{2}x-5$

It is a slope intercept form of a line, therefore the slope of the line is $\frac{1}{2}$.

(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 $\frac{1}{2}$.

The equation for line n is in the form of

$y=\frac{1}{2}x+c$

Where c can be any real number except -5.

An equation for line n is

$y=\frac{1}{2}x$

(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.

$y=\frac{1}{2}x-5$

(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 $\frac{1}{2}$.

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 $\frac{1}{2}$.

An equation for line r is

$y=x$