Question 61205
Don't Panic, it's not that hard.
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Bob is traveling home at a constant speed. After one-half hour, he is 77.5 miles from home and after one hour, he is 55 miles from home. Write a linear equation that gives the distance from home,y (in miles), in terms of the time x (in hours). How long will it take Bob to get home?
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Think of it this way:
 x1 = 1 (hrs); y1 = 55
 x2 = .5; y2 = 77.5
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From these coordinates he can find the slope: {{{m = (y2-y1)/(x2-x1)}}}
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{{{m = (77.5 - 55)/(.5 - 1)}}} = {{{(22.5)/(-.5)}}} = -45 is our slope
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Using the point slope formula: y - y1 = m(x - x1)
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y - 55 = -45(x - 1)
y - 55 = -45x + 45
y = -45x + 45 + 55
y = -45x + 100 is our linear equation
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When he's home the distance from home (y) = 0, find x
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-45x + 100 = 0
-45x = -100
x = -100/-45
x = +2.22 hours to get home
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Here is a qraph of the equation; x = number of hrs, y = distance from home.
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{{{ graph( 300, 200, -2, 3, -20, 120, -45x + 100) }}}
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Note all the information we can get from a simple equation derived from the
two points that they gave us: x1 = .5 hr, y1 = 77.5 mi & x2 = 1 hr; y2 = 55 mi
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The slope is just the amount of change in y for a change in x. In our example
1 hour change has a 45 mi change in distance. The fact that it is -45 means that the distance is decreasing (getting closer to home and he is driving 45 mph)
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Are you familiar with the y intercept? This occurs when x = 0, (the start of the journey). The graph crosses the y axis at y=100 (distance from home)
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When the graph crosses the x axis, then y = 0, (at home now) and x = 2.2 hrs the time required to get home.
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The fact that the graph is a straight line means he is driving the same speed thru out the journey.
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As an example using the graph, how far is he from home after 3/4 hr? Would you say around 65 miles.  We can find out exactly, of course, by using the equation and substituting .75 for x:  
y = -45(3/4)- 100
y = -33.75 + 100
y = 66.25 miles from home is the actual miles
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It's really quite wonderful how much information can be obtained from a simple linear equation and graph like. Hope this clarifies things for you