### Home > INT1 > Chapter 2 > Lesson 2.1.4 > Problem2-41

2-41.

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

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

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

Another method is to first subtract the $x$-values and the $y$-values from each other.
$\Delta x: 4 − 2 = 2$
$\Delta y: 1 − 5 = −4$

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

Substitute the differences into the slope formula.

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

See part (a).

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

Vertical lines have an undefined slope.

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

See part (a).