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For the points (3,-2) and (-5,-4) find:
\n" ); document.write( "the slope between them and the equation of the line that passes through them.
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\n" ); document.write( "the slope of the line is given by the equation (y2-y1)/(x2-x1).
\n" ); document.write( "let (3,-2) = (x1,y1)
\n" ); document.write( "let (-5,-4) = (x2,y2)
\n" ); document.write( "x1 = 3
\n" ); document.write( "y1 = -2
\n" ); document.write( "x2 = -5
\n" ); document.write( "y2 = -4
\n" ); document.write( "(y2-y1) = (-4) - (-2) = (-2)
\n" ); document.write( "(x2-x1) = (-5) - (3) = (-8)
\n" ); document.write( "(y2-y1)/(x2-x1) = (-2)/(-8) = (-1)/(-4) = (1/4)
\n" ); document.write( "your slope is (1/4).
\n" ); document.write( "equation for a line is y = m*x + b where:
\n" ); document.write( "m is the slope
\n" ); document.write( "b is the y-intercept (value of y when x = 0).
\n" ); document.write( "to find b, you take one of the points that you were given and substitute for y and x and solve.
\n" ); document.write( "take the point (x2,y2) which equals (-5,-4).
\n" ); document.write( "you have:
\n" ); document.write( "y = -4
\n" ); document.write( "x = -5
\n" ); document.write( "m = (1/4) which was calculated earlier.
\n" ); document.write( "substitute for x and y in the general equation of y = m*x + b to get
\n" ); document.write( "-4 = (1/4)*(-5) + b
\n" ); document.write( "multiply both sides of the equation by 4 to get:
\n" ); document.write( "-16 = (1) * (-5) + 4*b
\n" ); document.write( "which equals
\n" ); document.write( "-16 = -5 + 4*b
\n" ); document.write( "add 5 to both sides of the equation to get:
\n" ); document.write( "-11 = 4*b
\n" ); document.write( "divide both sides of the equation by 4 to get:
\n" ); document.write( "b = (-11/4)
\n" ); document.write( "you have m which is (1/4) and you have b which is (-11/4)
\n" ); document.write( "your equation is
\n" ); document.write( "y = (1/4)*x + (-11/4)
\n" ); document.write( "which becomes
\n" ); document.write( "y = (1/4)*x - (11/4)
\n" ); document.write( "a graph of this equation will look like this:
\n" ); document.write( "
\n" ); document.write( "your y intercept is (-11/4) which is the same as (-2.75). this is found by taking the general equation and making y = 0 and solving.
\n" ); document.write( "your x intercept is 11 which you find by taking the general equation and making x = 0 and solving.
\n" ); document.write( "both your original points are on this line as you can see from the graph.
\n" ); document.write( "your slope is (1/4) which you can find easily by taking the y intercept and the x intercept and solving for the slope.
\n" ); document.write( "the y intercept is (0,-11/4)
\n" ); document.write( "the x intercept is (11,0).
\n" ); document.write( "x1 = 0
\n" ); document.write( "y1 = -11/4
\n" ); document.write( "x2 = 11
\n" ); document.write( "y2 = 0
\n" ); document.write( "y2 - y1 = 0 - (-11/4) = 11/4
\n" ); document.write( "x2 - x1 = 11 - 0 = 11
\n" ); document.write( "(y2-y1) / (x2-x1) = (11/4) / 11 = (1/4) / 1 = (1/4).
\n" ); document.write( "everything checks out.
\n" ); document.write( "your slope is (1/4)
\n" ); document.write( "your equation is y = (1/4)*x - (11/4).
\n" ); document.write( " \n" ); document.write( "