Chapter 4.1, Problem 34E

To determine

To explain: an equation in slope-intercept form

Answer to Problem 34E

When $f\left(0\right)$ is constant and both x and y varies, then the equation of the line can be written in slope-intercept form since the slope will be defined.

Explanation of Solution

Calculation:

A line has y -intercept $f\left(0\right)$ and $\left(x,y\right)$ is a point on the line.

This implies that the slope-intercept equation of the line is,

  $y=mx+f\left(0\right)$

When $f\left(0\right)=0$ and x is constant but y varies, then the line is vertical.

Hence, the equation of the line cannot be written in slope-intercept form since the slope will be undefined.

When $f\left(0\right)$ is constant and both x and y varies, then the equation of the line can be written in slope-intercept form since the slope will be defined.

Conclusion:

Therefore, when $f\left(0\right)$ is constant and both x and y varies, then the equation of the line can be written in slope-intercept form since the slope will be defined.