On graph paper, make a complete graph of the line $y = 3x + 1$.

1. What is the slope angle of the line? That is, what is the acute angle the line makes with the $x$-axis?

   Answer (a):

   $\approx71.56^\circ$

2. Write the equation of a new line that has a slope angle of $45^\circ$ and passes through the point $(0, 3)$. Assume that the slope is positive.

   Hint (b):

   A $45^\circ$ angle means that $y$ and $x$ have a one to one ratio. What does that make the slope?

3. Solve for the intersection of these two lines using any method. Write your solution as a point in the form $(x, y)$.

   Hint (c):

   Use the Equal Values Method or substitution.