Chapter 2, Problem 1VR

Vocabulary Reinforcement

Complete each statement with the correct term from the column on the right. Some of the choices may be used more than once, and some may not be used at all.

* x-intercept

* y-intercept

* at least one

* exactly one

* slope-intercept

* point-slope

* slope

* function

* relation

* parallel

* perpendicular

* vertical

* horizontal

* domain

* range

The graph of $x=a$ is a(n) __________line with x-intercept $\left(a,0\right)$. [2.5c]

To determine

To fill: The blank space provided in the statement, “The graph of $x=a$ is a(n) _______ line with $X-$ intercept $\left(a,0\right)$” with the correct match from provided options.

Answer to Problem 1VR

Solution:

The graph of $x=a$ is a vertical line with $X-$ intercept $\left(a,0\right)$.

Explanation of Solution

Given Information:

The provided options are,

1. $X-$ intercept

2. $Y-$ intercept

3. at least one

4. exactly one

5. slope-intercept

6. point slope

7. slope

8. function

9. relation

10. parallel

11. perpendicular

12. vertical

13. horizontal

14. domain

15. range

Here, the equation of line is $x=a$.

Now, the equation of line $x=a$ has no term with $y$ variable, so for any value of $y$, the value of $x$ is constant, i.e. $a$.

Now, while calculating the slope of the equation of line $x=a$, change in $x$ values (denominator) is $0$ because the value of $x$ is constant.

Thus, the slope is not defined and the graph will be a vertical line passing through $\left(a,0\right)$.

For example:

Consider an equation of line, $x=3$

Now, the graph of line $x=3$ is,

From the graph, it is clear that the line of equation $x=3$ is vertical with $X-$ intercept $\left(3,0\right)$.

Hence, the graph of $x=a$ is a vertical line with $X-$ intercept $\left(a,0\right)$.