Without graphing, find the slope of each line described below.  

1. A line that goes through the points $(4,1)$ and $(2,5)$.

   Hint (a):

   Use a slope triangle or another method to determine the slope of the line.

   Step 1(a):

   Another method is to first subtract the $x$-values and the $y$-values from each other.
   $Δx{:} \; 4 - 2 = 2$
   $Δy{:} \; 1 - 5 = -4$

   Step 2(a):

   $\frac{\Delta\text{y}}{\Delta\text{x}}=\frac{-4}{-2}=-2$

   Substitute the differences into the slope formula.

2. A line that goes through the origin and the point $(10,5).$

   Hint (b):

   See part (a).

3. A vertical line (one that travels “up and down”) that goes through the point $(6,-5)$.

   Hint (c):

   Vertical lines have an undefined slope.

4. A line that goes through the points $(1,6)$ and $(10,6)$.

• Hint (d):

  See part (a).