Chapter 8.3, Problem 27E

To determine

To write:

An equation of line that has no x -intercept and an equation of line that has no y -intercept. Describe the graph of each equation.

Answer to Problem 27E

The equation $y=3$ has no x -intercept.

The equation $x=4$ has no y -intercept.

Explanation of Solution

Calculation:

We know that a horizontal line has no x -intercepts as horizontal lines are parallel to x -axis. The equation of a horizontal line is in form $y=b$ , and the line intersects y -axis at point $(0,b)$ .

Let us say that our horizontal line intersects y- axis at point (0,3), so the equation of our line would be $y=3$ .

Upon graphing our equation, we will get our required graph as shown below:

We know that a vertical line has no y -intercepts as vertical lines are parallel to y -axis. The equation of a vertical line is in form $x=a$ , and the line intersects x -axis at point $(a,0)$ .

Let us say that our vertical line intersects x- axis at point (0,4), so the equation of our line would be $x=4$ .

Upon graphing our equation, we will get our required graph as shown below: