Chapter 8.7, Problem 36HP

To determine

To calculate: To describe a line that has a y-intercept but no x-intercept and then identify the slope of the line

Answer to Problem 36HP

Aline that has y-intercept but no x-intercept is parallel to x-axis. Slope of line parallel to x-axis is zero.

Explanation of Solution

Given information: Aline that has a y-intercept but no x-intercept

Formula Used:

Slope intercept form of equation of line is

  $y=mx+c$

Where

  $m=$ Slope of line

  $c=$ y-intercept

Calculation:

Given a line that has a y-intercept but no x-intercept

This means that line is parallel to x-axis.

Example of such lines:

  $y=4$

To find the slope of line, rewrite the equation of line and then compare with the slope-intercept form of line

Rewriting $y=4$ ,

  $y=0x+4$

Now, comparing the above equation with slope intercept form of line: $y=mx+c$

  $m=0$

Hence, slope is $0$

Conclusion:

Hence, a line that has y-intercept but no x-intercept is parallel to x-axis. Slope of line parallel to x-axis is zero.