Question

find the equation of the line passing through the origin and making a 45° angle with the x - axis.
y = □ (type an exact answer, using radicals as needed.)

Explanation:

Step1: Find the slope

The slope $m$ of a line making an angle $\theta$ with the $x - axis$ is given by $m=\tan\theta$. Here $\theta = 45^{\circ}$, so $m=\tan45^{\circ}=1$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Since the line passes through the origin $(0,0)$ where $x_1 = 0$ and $y_1 = 0$ and $m = 1$, we substitute these values into the formula: $y-0 = 1\times(x - 0)$.

Answer:

$y=x$