Chapter 8.3, Problem 24WE

To determine

To calculate: The slope of the line,

  $3x-5=0$

Answer to Problem 24WE

Theslope of the lineundefined that means the line has no slope.

Explanation of Solution

Given information:

Theequation of the lines:

  $3x-5=0$

Formula used:

For finding the slope of the line:

  $m=\frac{y_2-y_1}{x_2-x_1}$ .

Calculation:

Consider the equation of line,

  $3x-5=0$

The general equation of line is:

  $ax+b=y$

Here in this form this equation becomes:

  $\begin{array}{l}ax+b=y\\ 3x-5=0\end{array}$

Rewrite the equation:

  $\begin{array}{c}3x-5=0\\ 3x=5\\ x=\frac{5}{3}\end{array}$

Here no $y$ points in the equation,

For finding the slope of line when apply values in the formula,

  $m=\frac{y_2-y_1}{x_2-x_1}$ :

Observe that, the result will found here is rational value and as we know the slope of rational value where is no $y-$ intercepts.

So the slope of the equation $3x-5=0$ is undefined.

Line $3x-5=0$ has no slope.

The vertical line where is no $y-$ intercepts there is the value of $m$ is undefined.

The graph of the line is vertical line through $3x-5=0$ .

A line that no rises , the slope of that line is undefined.

Thus, the slope of the line is undefined that means a line $3x-5=0$ has no slope.