Question

slope = \frac{vertical change}{horizontal change} = \frac{rise}{run}
types of slope
positive (increasing from left to right), negative (decreasing from left to right), zero (horizontal line, not increasing or decreasing from left to right), undefined (vertical line, line does not run to the left or right)
m = \frac{2}{3}
find the slope of each line

1. graph of a line on coordinate plane m = \frac{1}{2}
2. graph of a line on coordinate plane m = \frac{-2}{2}
3. graph of a line on coordinate plane m = \frac{-4}{3}
4. graph of a line on coordinate plane m = \frac{-3}{4}

Explanation:

Step1: Identify rise/run for Line 1

From the graph, vertical change (rise) = 1, horizontal change (run) = 2.
$m = \frac{1}{2}$

Step2: Simplify slope for Line 2

Vertical change = -2, horizontal change = 2. Simplify the fraction.
$m = \frac{-2}{2} = -1$

Step3: Simplify slope for Line 3

Vertical change = -4, horizontal change = 3. The fraction is already in simplest form.
$m = \frac{-4}{3}$

Step4: Verify slope for Line 4

Vertical change = -3, horizontal change = 4. The fraction is already in simplest form.
$m = \frac{-3}{4}$

Answer:

1. $m = \frac{1}{2}$
2. $m = -1$
3. $m = \frac{-4}{3}$
4. $m = \frac{-3}{4}$