Chapter 1.1, Problem 114E

To determine

Explain whether every line be written in slope intercept form.

Answer to Problem 114E

No, every line cannot be written in slope intercept form.

Explanation of Solution

Given:

It is given in the question that every line be written in slope intercept form.

Concept Used:

In this, use the common sense to understand the question and also have some basic concept of chapter.

Calculation:

Lines that “rise” or “fall” or are horizontal when observed from left to right have a defined slope and a y − intercept.

The slope is calculated using any two points on the line with $m=\frac{changeiny}{changeinx}$ ,because for any given x ,there is only one corresponding y such that (x,y) lies on the line.

The y − intercept has the y − coordinate that corresponds to $x=0$

These lines can have equation of the form $y=mx+c$ (m = slope, c = y − intercept coordinate).

Vertical lines are lines that contain points (x,y) where x can only be one number (an infinite number of y − coordinates are associated with the one value of x).

If we take any two points on such a line, there is no change in x , (the change in x is $0$ ) so the above formula for m does not apply, Slope m is undefined for vertical lines.

So, no, not all lines can have slope − intercept forms.

Conclusion:

No, every line cannot be written in slope intercept form.