document.write( "Question 95944: Give the slope-intercept form of the equation for the line on which these two points lie: (4, -2) and (3, 8) \n" ); document.write( "
Algebra.Com's Answer #69889 by bucky(2189)\"\" \"About 
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The slope-intercept form of an equation is:
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\n" ); document.write( "y = mx + b
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\n" ); document.write( "in which m is the slope and b is the value of y at the point on the y-axis where the graph
\n" ); document.write( "intersects the y-axis.
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\n" ); document.write( "We know that the two points (4, -2) and (3, 8) will satisfy the equation. So we can establish
\n" ); document.write( "two equations, one for each point.
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\n" ); document.write( "For the first point we substitute 4 for x and -2 for y in the slope-intercept form. This
\n" ); document.write( "results in:
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\n" ); document.write( "-2 = m4 + b
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\n" ); document.write( "Rearranging this into a more standard form results in:
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\n" ); document.write( "4m + b = -2 <==== remember this as \"equation 1\"
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\n" ); document.write( "Now let's do the same thing for the second point. In the second point x = 3 and y = 8.
\n" ); document.write( "Substituting these values into the slope-intercept form of y = mx + b results in:
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\n" ); document.write( "8 = m3 + b
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\n" ); document.write( "Rearrange this into a more standard form results in:
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\n" ); document.write( "3m + b = 8 <==== remember this as \"equation 2\"
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\n" ); document.write( "So now we have two independent equations (equation 1 and equation 2) as follows:
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\n" ); document.write( "4m + b = -2
\n" ); document.write( "3m + b = 8
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\n" ); document.write( "Suppose we subtract these two equations vertically. 4m minus 3m results in just m. Then
\n" ); document.write( "b minus b is zero. Finally -2 minus 8 is -10. Therefore, this subtraction is:
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\n" ); document.write( "m = -10
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\n" ); document.write( "Now we can substitute this value for m into either of the two equations and solve the
\n" ); document.write( "resulting equation for b. For example, let's take the equation 4m + b = -2. When we substitute
\n" ); document.write( "-10 for m the equation becomes:
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\n" ); document.write( "4(-10) + b = -2
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\n" ); document.write( "Doing the multiplication on the left side results in:
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\n" ); document.write( "-40 + b = -2
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\n" ); document.write( "Get rid of the -40 on the left side by adding +40 to both sides of the equation. When you
\n" ); document.write( "add 40 to both sides the result is:
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\n" ); document.write( "b = -2 + 40 = +38
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\n" ); document.write( "So now we know that m = -10 and b = 38. Substitute these two values into the slope-intercept
\n" ); document.write( "form y = mx + b and the equation becomes:
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\n" ); document.write( "y = -10x + 38
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\n" ); document.write( "This is the equation you are looking for. You can check this equation by substituting
\n" ); document.write( "the two points, one at a time, into this resulting equation and we should see that this
\n" ); document.write( "equation balances for each of the points.
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\n" ); document.write( "Take the point (4, -2) which has x = 4 and y = -2. Substitute these values into the equation
\n" ); document.write( "y = -10x + 38. When you substitute 4 for x and -2 for y this equation becomes:
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\n" ); document.write( "-2 = -10(4) + 38
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\n" ); document.write( "Multiply on the right side to get:
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\n" ); document.write( "-2 = -40 + 38
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\n" ); document.write( "Combining the terms on the right side results in:
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\n" ); document.write( "-2 = -2
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\n" ); document.write( "So the point (4, -2) satisfies our answer.
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\n" ); document.write( "Now let's try our answer y = -10x + 38 using the point (3, 8). Substitute 3 for x and 8 for
\n" ); document.write( "y and our answer becomes:
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\n" ); document.write( "8 = -10(3) + 38
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\n" ); document.write( "After doing the multiplication on the right side this equation becomes:
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\n" ); document.write( "8 = -30 + 38
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\n" ); document.write( "Combining the two terms on the right side results in:
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\n" ); document.write( "8 = 8
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\n" ); document.write( "So the point (3, 8) also satisfies our answer.
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\n" ); document.write( "Since both points satisfy our answer, we can say that it is a correct answer for the conditions
\n" ); document.write( "set up in the problem. The answer to this problem is:
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\n" ); document.write( "y = -10x + 38
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\n" ); document.write( "Hope this helps you to understand the problem and one way of solving it.
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