Find an equation for each of the lines described below.

1. The line with slope $\frac { 1 } { 3 }$ that goes through the point $\left(0, 5\right)$.

   Hint (a):

   Use slope-intercept form.

2. The line parallel to $y = 2x − 5$ that goes through the point $\left(1, 7\right)$.

   Hint (b):

   Parallel lines have the same slope. Use the point-slope form of the equation of a line.

3. The line perpendicular to $y = 2x − 5$ that goes through the point $\left(1, 7\right)$.

   Hint (c):

   The slopes of perpendicular lines are opposite reciprocals.

4. The line that goes through the point $\left(0, 0\right)$ so that the tangent of the angle it makes with the $x$-axis is $2$.

   Hint (d):

   Remember the trigonometric relationships.

   More Help (d):

   How might tangent's relationship to the opposite and adjacent sides relate to the rise and run of the slope?