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 move to the left or right
m = \frac{2}{3}
find the slope of each line
1)
graph of a line through the origin with a positive slope
m = \frac{\boxed{1}}{\boxed{2}}
2)
graph of a line with a negative slope
m = \frac{\boxed{-2}}{\boxed{2}}
3)
graph of a line with a positive slope
m = \frac{\boxed{-4}}{\boxed{}}
4)
graph of a line with a negative slope
m = \frac{\boxed{}}{\boxed{4}}

Explanation:

Step1: Identify rise/run for Q1

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

Step2: Simplify slope for Q2

Simplify the given slope fraction.
$m=\frac{-2}{2}=-1$

Step3: Find run for Q3

From the graph, horizontal change (run) = 3 for rise = -4.
$m=\frac{-4}{3}$

Step4: Find rise for Q4

From the graph, vertical change (rise) = -3 for run = 4.
$m=\frac{-3}{4}$

Answer:

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