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.

(a) Equation of line n is . (b)  Equation of line p is . (c)  Equation of line r is .

Explanation:

The equation of line m is

It is a slope intercept form of a line, therefore the slope of the line is .

(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 .

The equation for line n is in the form of

Where c can be any real number except -5.

An equation for line n is

(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.

(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 .

The equation for line r is in the form of

Where c can be any real number and m can be any real number except .

An equation for line r is

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