When the graph reaches his point
It is linear because both variables have an exponent of 1. (FYI: one of the exponents can be 0 and still be a linear equation).
2x + y = 8
<u>-2x </u> <u> -2x</u>
y = -2x + 8 ⇒ slope (m) = -2 and y-intercept (b) = 8
plot the y-intercept (0, 8). then plot the next point by counting the rise over run from the y-intercept. <em>count 2 units down and 1 unit to the right </em>= (1, 6).
The extreme slope of the approach to the vertical asymptote suggests a log function. The plain log function will have x=0 as its vertical asymptote and will go through the point (1, 0). The base of the logarithm (b) can be determined by the fact that a log function will go through the point (b, 1). The graph has negative slope, also suggesting the function is reflected across the x-axis.
After we vertically reflect across y=0 and shift your graph to the right one place, it goes through the points (1, 0) and (2, 1). This tells us it is ...
<h3>
Answer:</h3><h3>
slower cyclist = 14 mph</h3><h3>
faster cyclist = 22 mph</h3>
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Work Shown:
x = rate of slower cyclist
x+8 = rate of faster cyclist, since this person travels 8 mph faster
After 4 hours, the slower cyclist covers 4x miles while the faster cyclist covers 4(x+8) = 4x+32 miles. In total, they cover 4x+4x+32 = 8x+32 miles. In other words, this is the distance between them after 4 hours.
Set this equal to 144 and solve
8x+32 = 144
8x = 144-32
8x = 112
x = 112/8
x = 14 is the slower cyclist's speed in mph
x+8 = 14+8 = 22 is the faster cyclist's speed in mph
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as a check:
distance = rate*time = 4*14 = 56 miles is covered by the slower cyclist
d = r*t = 4*22 = 88 miles is covered by the faster cyclist
56+88 = 144 miles is the total distance between the two cyclists after 4 hrs
the answers are confirmed