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Chapter 3: Problem 45

Find the slope of each vertical or horizontal line

Short Answer

Expert verified
The slope of any horizontal line is 0, while the slope of any vertical line is undefined.

Step by step solution

01

Identifying the line type

The first thing that should be done is recognizing whether the line is vertical or horizontal. For a horizontal line, the y-coordinates will be the same across the line. Conversely, for a vertical line, the x-coordinates will remain constant.
02

Calculating the slope for a horizontal line

Given a horizontal line, its slope can be determined using the formula for slope which is \(m = \frac{\Delta y}{\Delta x}\). However, since for a horizontal line \(\Delta y = 0\), the slope of any horizontal line will therefore be 0.
03

Calculating the slope for a vertical line

For a vertical line, the x-values stay constant and the line goes straight up and down, so \(\Delta x = 0\). Therefore, when we try to apply the same formula for slope \(m = \frac{\Delta y}{\Delta x}\), we get a zero in the denominator. Since division by zero is undefined in mathematics, the slope of a vertical line is considered undefined.

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Most popular questions from this chapter

Express each variation as an equation. Then find the requested value. Assume that all variables represent positive numbers. \(x\) varies directly with \(c^{2}\) and inversely with \(f .\) If \(x=16\) when \(c=8\) and \(f=12,\) find \(x\) when \(c=10\) and \(f=5\).

If points \(P(a, b)\) and \(Q(c, d)\) are two points on a rectangular coordinate system and point \(M\) is midway between them, then point \(M\) is called the midpoint of the line segment joining \(P\) and \(Q .\) (See the illustration on the following page. To find the coordinates of the midpoint \(M\left(x_{M}, y_{M}\right)\) of the segment PQ, we find the average of the \(x\) -coordinates and the average of the \(y\)-coordinates of \(P\) and \(Q\). $$x_{M}=\frac{a+c}{2}$$ and $$y_{M}=\frac{b+d}{2}$$ Find the coordinates of the midpoint of the line segment with the given endpoints. $$P(2,-7) \text { and } Q(-3,12)$$

Express each inverse variation as an equation. Then find the requested value. Assume that all variables represent positive numbers. SEE EXAMPLE 2. (OBJECTIVE 2) \(V\) varies inversely with \(p .\) If \(V=60\) when \(p=12,\) find \(V\) when \(p=9\).

If points \(P(a, b)\) and \(Q(c, d)\) are two points on a rectangular coordinate system and point \(M\) is midway between them, then point \(M\) is called the midpoint of the line segment joining \(P\) and \(Q .\) (See the illustration on the following page. To find the coordinates of the midpoint \(M\left(x_{M}, y_{M}\right)\) of the segment PQ, we find the average of the \(x\) -coordinates and the average of the \(y\)-coordinates of \(P\) and \(Q\). $$x_{M}=\frac{a+c}{2}$$ and $$y_{M}=\frac{b+d}{2}$$ Find the coordinates of the midpoint of the line segment with the given endpoints. \(A(8,-6)\) and the origin

Express each sentence as a formula. For a fixed area, the length \(l\) of a rectangle varies inversely with its width \(w\).
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