document.write( "Question 61205: Please reply ASAP!!!!Help me!!!!
\n" ); document.write( "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?
\n" ); document.write( "Please answer this question AS SOON AS POSSIBLE!!!I'm REALLY CONFUSED AND FRUSTRATED WITH MY ALGEBRA HOMEWORK!!!!!! \n" ); document.write( "
Algebra.Com's Answer #42136 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
Don't Panic, it's not that hard.
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\n" ); document.write( "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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\n" ); document.write( "Think of it this way:
\n" ); document.write( " x1 = 1 (hrs); y1 = 55
\n" ); document.write( " x2 = .5; y2 = 77.5
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\n" ); document.write( "From these coordinates he can find the slope: \"m+=+%28y2-y1%29%2F%28x2-x1%29\"
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\n" ); document.write( "\"m+=+%2877.5+-+55%29%2F%28.5+-+1%29\" = \"%2822.5%29%2F%28-.5%29\" = -45 is our slope
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\n" ); document.write( "Using the point slope formula: y - y1 = m(x - x1)
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\n" ); document.write( "y - 55 = -45(x - 1)
\n" ); document.write( "y - 55 = -45x + 45
\n" ); document.write( "y = -45x + 45 + 55
\n" ); document.write( "y = -45x + 100 is our linear equation
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\n" ); document.write( "When he's home the distance from home (y) = 0, find x
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\n" ); document.write( "-45x + 100 = 0
\n" ); document.write( "-45x = -100
\n" ); document.write( "x = -100/-45
\n" ); document.write( "x = +2.22 hours to get home
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\n" ); document.write( "Here is a qraph of the equation; x = number of hrs, y = distance from home.
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\n" ); document.write( "\"+graph%28+300%2C+200%2C+-2%2C+3%2C+-20%2C+120%2C+-45x+%2B+100%29+\"
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\n" ); document.write( "Note all the information we can get from a simple equation derived from the
\n" ); document.write( "two points that they gave us: x1 = .5 hr, y1 = 77.5 mi & x2 = 1 hr; y2 = 55 mi
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\n" ); document.write( "The slope is just the amount of change in y for a change in x. In our example
\n" ); document.write( "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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\n" ); document.write( "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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\n" ); document.write( "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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\n" ); document.write( "The fact that the graph is a straight line means he is driving the same speed thru out the journey.
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\n" ); document.write( "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:
\n" ); document.write( "y = -45(3/4)- 100
\n" ); document.write( "y = -33.75 + 100
\n" ); document.write( "y = 66.25 miles from home is the actual miles
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\n" ); document.write( "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\r
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