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You can put this solution on YOUR website!
\n" ); document.write( "The matrix/determinant solution given by tutor @alan3354 is useful for more complex problems, but it seems a lot of work for this rather elementary problem.
\n" ); document.write( "Both of the other tutors who responded used a formula to find the slope of the line and then used the point-slope form of the equation to find the specific equation of the line in your example.
\n" ); document.write( "Those are valid ways to solve the problem. But I have some suggestions for alternative methods that you might want to try.
\n" ); document.write( "First: Finding the slope determined by the two given points.
\n" ); document.write( "There is a simple formula for slope:
\n" ); document.write( "Yes, a simple formula; but it is easy to get numbers in the wrong places and end up with the wrong slope, which of course makes any subsequent work you do on the problem a waste of time.
\n" ); document.write( "I always suggest to students that they at least mentally, if not on paper, make a sketch of the two points and use the sketch to find the slope by comparing the x and y coordinates of the two given points. Specifically, for the given points (-1,-13) and (1,3) in your problem, I think the safest way to find the slope is as follows:
\n" ); document.write( "Slope is the ratio of how fast the graph changes vertically and how fast it changes horizontally: \"slope = rise / run\". More specifically, I always think of it as measuring how far the graph goes up or down each time I move 1 unit to the right. So
\n" ); document.write( "(1) Since I always think of moving left to right, my \"first\" point will be the one that is farther left -- i.e., has the smaller x coordinate. So (-1,-13) is my \"first\" point and (1,3) is my second point.
\n" ); document.write( "(2) From the first point to the second, the x value changes from -1 to +1, a change of 2: the graph moved 2 units horizontally; the \"run\" is 2.
\n" ); document.write( "(3) From the first point to the second, the y value changes from -13 to +3, a change of 16: the graph moved up 16 units; the \"rise\" is 16.
\n" ); document.write( "(4) The slope is \"rise\"/\"run\" = 16/2 = 8.
\n" ); document.write( "You will make far fewer mistakes in finding slopes of lines if you use this method instead of plugging numbers into a magic formula.
\n" ); document.write( "Second: Finding the equation of the line
\n" ); document.write( "While use of the point-slope form of the equation of a line to finish finding the specific equation for a particular example is fine, in my experience more students find it easier to use the slope-intercept form. For your particular problem, it would go like this:
\n" ); document.write( "Plug the given x and y coordinates of one of the given points into the basic slope-intercept equation and solve for b:
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\n" ); document.write( "Now you have both the slope and the y-intercept; the equation of the line is y = 8x-5. \n" ); document.write( "