Chapter 13.7, Problem 31WE

To determine

To find : an equation of line described

Answer to Problem 31WE

The equation is $y=x$

Explanation of Solution

Given information :

The line through $\left(5,5\right)$ that’s makes an $45°$ angle measured counterclockwise from the positive $x$ -axis

Formula used :

  $y-y_1=m\left(x-x_1\right)$

Calculation :

Let $\theta =45°$

The slope

  $\begin{array}{l}\tan \theta \\ =\tan 45°\\ =1\end{array}$

Therefore, the slope is $1$ .

Using $\left(5,5\right)$ , the equation is

  $\begin{array}{l}y-5=1\left(x-5\right)\\ y=x-5+5\\ y=x+0\\ y=x\end{array}$

Hence, the equation is $y=x$ .