Without graphing, calculate 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.
   $\Delta x: 4 − 2 = 2$
   $\Delta y: 1 − 5 = −4$

   Step 2(a):

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

   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 is “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).