document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205628>Question 1205628</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PIA is concerned about the decreasing number pf passengers. It’s trying<BR>\n" );
document.write( "to find the linear relationship between number of passengers and the<BR>\n" );
document.write( "time in years since the last five years.<BR>\n" );
document.write( "Let n = number of passengers travelling by PIA (Plotted on Y-Axis)<BR>\n" );
document.write( "And t = time in years since 2019 (t = 0) (Plotted on X-Axis)<BR>\n" );
document.write( "It was found that in 2019 the number was 245,000 whereas in 2023 the<BR>\n" );
document.write( "number decreased to 215,000.<BR>\n" );
document.write( "Required:<BR>\n" );
document.write( "1. Find the linear function in slope-intercept form: n = mt + k<BR>\n" );
document.write( "2. Find the X-intercept (t-intercept) and Y-intercept (n-intercept) and<BR>\n" );
document.write( "explain their meaning.<BR>\n" );
document.write( "3. Make a graph on a graph paper of the Linear function found in part<BR>\n" );
document.write( "(a). On the graph indicate the X & Y intercepts. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842549 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=842549\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> in 2019 they had 245000 passengers.<BR>\n" );
document.write( "in 2023 they had 215000 passengers.\r<BR>\n" );
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document.write( "2023 is 4 years from 2019.\r<BR>\n" );
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document.write( "245000 minus 215000 = 30000.<BR>\n" );
document.write( "they had 30000 less passengers in 2023 than in 2019.\r<BR>\n" );
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document.write( "the slope intercept form of the linear equation is y = mx + b.<BR>\n" );
document.write( "m is the slope.<BR>\n" );
document.write( "b is the y-intercept\r<BR>\n" );
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document.write( "slope is the change in y divided by the change in x.<BR>\n" );
document.write( "y is the number of passengers<BR>\n" );
document.write( "x is the number of years\r<BR>\n" );
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document.write( "slope = (245000 - 215000) / (2023 - 2019) = -30000 / 4 = -7500.<BR>\n" );
document.write( "that's a loss of an average of 7500 passengers per year.\r<BR>\n" );
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document.write( "formula becomes y = -7500 * x + b<BR>\n" );
document.write( "to solve for b, take any 2 points on the line.<BR>\n" );
document.write( "the two points on the line are (0,245000) and (4,215000)<BR>\n" );
document.write( "that's 245000 in 2019 and 215000 in 2023.<BR>\n" );
document.write( "we'll use (0,245000).<BR>\n" );
document.write( "we could use either point and get the same answer.<BR>\n" );
document.write( "with (0,245000), y = -7500 * x + b becomes 245000 = -7500 * 0 + b<BR>\n" );
document.write( "solve for b to get 245000.<BR>\n" );
document.write( "with (4,215000), 215000 = -7500 * 4 + b<BR>\n" );
document.write( "add 4 * 7500 to both sides of the equation to get 215000 + 30000 = b<BR>\n" );
document.write( "this results in b = 245000, same as we got from the other set of points on the line.\r<BR>\n" );
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document.write( "the linear equation is y = -7500 * x + 245000\r<BR>\n" );
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document.write( "x and y are used for graphing.<BR>\n" );
document.write( "if you replace y with n and x with t, the formula becomes n = -7500 * t + 245000.<BR>\n" );
document.write( "you get the same answer, just with different variables to represent the values.\r<BR>\n" );
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document.write( "the y-intercept is the value of y when x is 0.<BR>\n" );
document.write( "you get y-intercept is 245000.<BR>\n" );
document.write( "the coordinate point is (0,245000).\r<BR>\n" );
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document.write( "the x-intercept is the value of x when y is 0.<BR>\n" );
document.write( "to find that, take the equation and set y equal to 0 and solve for x.<BR>\n" );
document.write( "the equation of y = -7500 * x + 245000 becomes:<BR>\n" );
document.write( "0 = -7500 * x + 245000<BR>\n" );
document.write( "add 7500 * x to both sides of the equation to get:<BR>\n" );
document.write( "7500 * x = 245000<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 245000 / 7500 = 32.667 rounded to 3 decimal places, as shown on the graph.\r<BR>\n" );
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document.write( "here's what the graph looks like.\r<BR>\n" );
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document.write( "the y-intercept is the number of passengers in year 0, which is 2019.<BR>\n" );
document.write( "that's the starting point of the analysis.\r<BR>\n" );
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document.write( "the x-intercept represents when the number of passengers becomes 0.<BR>\n" );
document.write( "based on the equation, 7500 is subtracted from the total each year until the number of passengers becomes 0.<BR>\n" );
document.write( "that occurs between the the thirty second and thirty third year from 2019.<BR>\n" );
document.write( "that would be between the year 2051 and 2052.\r<BR>\n" );
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