### Home > CCAA8 > Chapter 2 Unit 2 > Lesson CCA: 2.1.4 > Problem2-42

2-42.

Without graphing, find 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.
$Δx:4−2=2$
$Δy:1−5=−4$

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

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 travels “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).