Chapter 4.3, Problem 34E

To determine

To calculate: To determine whether the statement is always, sometimes or never true.

Answer to Problem 34E

Thestatement is always true

Explanation of Solution

Given: Statement is “A vertical line is parallel to the y-axis”

Formula Used:

When two lines are perpendicular, then the product of their slopes is equal to $-1$

When two lines are parallel, then the lines have equal slope

Calculation:

Statement is given as follows:

“A vertical line is parallel to the y-axis”

Equation of y-axis is $y=c$

Now, Slope of equation of y-axis, $m_1=0$

Consider the equation of vertical line as follows:

  $y=c$

Now,Slope of equation of vertical line, $m_2=0$

Since the slopes of vertical line and y-axis is same.

Thus, vertical line is parallel to y-axis

Thus, the statement is always true

Conclusion:

Hence, thestatement is always true