1.as we have differents slopes, it means he had differents speeds
2) rates of change
AB is 5
CD is 5
EF is -1.25
BC is 2.5
DE is 0
FG is -4.16666
3) AB and CD
Explanation
when you have a graph where
x-axis=time
y-axis = distance
the rate of change is the speed, then
so
[tex]\text{slope}=\frac{\Delta y}{\Delta x}=\frac{change\text{ in distance}}{\text{change in time}}=speed[/tex]
Step 1
why are some line segments on the graph sleeper than others?
as we have differents slopes, it means he had differents speeds
Step 2
speed of each line segment
a)rate of change AB
A=(0,0) origin
B=(4,20)
find the speed( slope)
[tex]\text{slope}=\frac{\Delta y}{\Delta x}=\frac{change\text{ in distance}}{\text{change in time}}=\frac{y_2-y_1}{x_2-x_1}=\frac{20-0}{4-0}=\frac{20}{4}=5[/tex]
it means, the rate of change in AB is 5
b)rate of change CD
C=(12,40)
D=(16,60)
find the slope
[tex]\text{slope}=\frac{\Delta y}{\Delta x}=\frac{change\text{ in distance}}{\text{change in time}}=\frac{y_2-y_1}{x_2-x_1}=\frac{60-40}{16-12}=\frac{20}{4}=5[/tex]
it means, the rate of change in CD is 5
c)rate of change EF
E=(20,60)
F=(28,50)
find the slope
[tex]\text{slope}=\frac{\Delta y}{\Delta x}=\frac{change\text{ in distance}}{\text{change in time}}=\frac{y_2-y_1}{x_2-x_1}=\frac{50-60}{28-20}=\frac{-10}{8}=-\frac{5}{4}=-1.25[/tex]
it means, the rate of change in EF is -1.25
d)rate of change BC
B=(4,20)
C=(12,40)
find the slope
[tex]\text{slope}=\frac{\Delta y}{\Delta x}=\frac{change\text{ in distance}}{\text{change in time}}=\frac{y_2-y_1}{x_2-x_1}=\frac{40-20}{12-4}=\frac{20}{8}=2.5[/tex]
it means, the rate of change in BC is 2.5
e)Rate of change DE
D=(16,60)
E=(20,60)
find the slope
[tex]\text{slope}=\frac{\Delta y}{\Delta x}=\frac{change\text{ in distance}}{\text{change in time}}=\frac{60-60}{20-16}=\frac{0}{4}=0[/tex]
it means, the rate of change in DE is 0
f)rate of change change FG
F=(28,50)
G=(40,0)
find the slope
[tex]\begin{gathered} \text{slope}=\frac{\Delta y}{\Delta x}=\frac{change\text{ in distance}}{\text{change in time}}=\frac{0-50}{40-28}=\frac{-50}{12}=-4.16666 \\ \end{gathered}[/tex]
it means, the rate of change in FG is -4.16666
Step 3
what interval is the fastest?
the fastest interval is when you have the bigger slope , then
[tex]AB\text{ and CD}[/tex]
because the speed is 5
