Question

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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:

n is $y=\frac{1}{2}x+b$, p is $y=\frac{1}{2}x-5$, and r has infinitely many different lines that have this property.

Step-by-step explanation:

If two lines have no solutions, that means that they are parallel. The slopes of two lines are the same if they are parallel. So n's slope is $\frac{1}{2}$. The y-intercept can be anything except -5, or +b. If two lines have infinitely many solutions, those two lines are exactly the same. So p is just m. If two lines have one and only one solution, that just means the slopes and y-intercepts are different. Since we don't know anything else about line r, we an't model an equation for it.