We solve this by the definition of slope in analytical geometry. The definition of slope is the rise over run. In equation, that would be
m = Δy/Δx = (y₂-y₁)/(x₂-x₁)
The x-coordinates here are the t values, while the y-coordinates are the f(t) values. So, let's find the y values of the boundaries.
At t=2: f(t)= 0.25(2)²<span> − 0.5(2) + 3.5 = 3.5
Point 1 is (2, 3.5)
At t=6: </span>f(t)= 0.25(6)² − 0.5(6) + 3.5 = 9.5
Point 2 is (6, 9.5)
The slope would then be
m = (9.5-3.5)/(6-2)
m = 1.5
Hence, the slope is 1.5. Interpreting the data, the rate of change between t=2 and t=6 is 1.5 thousands per year.
Since 5 is positive and it is one of the counting numbers, 5 is a rational, integer and natural number. 5 is not an irrational number.
Since 1/4 is a rational number, 1/4 is not an irrational number
Since 1.25 is a rational number, 1.25 is not an irrational number.
-.4 is greater than -5/6 —(-.4=-4/10 or -2/5) (-2/5*6/6= -12/30 and -5/6*5/5= -25/30)
