121616949-math.19

# 121616949-math.19 - 1.1 Lines 5 miles to Seattle and after...

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1.1 Lines 5 miles to Seattle, and after driving another half-hour you pass a sign saying it is 85 miles to Seattle. Using the horizontal axis for the time t and the vertical axis for the distance y from Seattle, graph and find the equation y = mt + b for your distance from Seattle. Find the slope, y -intercept, and t -intercept, and describe the practical meaning of each. The graph of y versus t is a straight line because you are traveling at constant speed. The line passes through the two points (1 , 110) and (1 . 5 , 85). So its slope is m = (85 - 110) / (1 . 5 - 1) = - 50. The meaning of the slope is that you are traveling at 50 mph; m is negative because you are traveling toward Seattle, i.e., your distance y is decreasing . The word “velocity” is often used for m = - 50, when we want to indicate direction, while the word “speed” refers to the magnitude (absolute value) of velocity, which is 50 mph. To find the equation of the line, we use the point-slope formula: y - 110 t - 1 = - 50 , so that y = - 50( t - 1) + 110 = - 50 t + 160 .
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