document.write( "Question 57878: write the equation of a line that goes through the points (2,0) and (0,2). \n" ); document.write( "

Algebra.Com's Answer #39547 by hayek(51) $\"\"$ $\"About$

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If it's a straight line, we know the equation has this form:
\n" ); document.write( " $\"y=mx%2Bb\"$ where m is the slope and b is the y-intercept. We just need to determine m and b, two unknowns. So, we need two equations, which are supplied by the problem. The problem gives us two points the line goes through, so the equation for the line must be satisfied for each of those points. Just plug each point into the equation:\r
\n" ); document.write( "\n" ); document.write( "line through (2,0): $\"0=m%282%29%2Bb\"$ , which simplifies to: $\"2m=-b\"$
\n" ); document.write( "line through (0,2): $\"2=m%280%29%2Bb\"$ , which simplifies to: $\"2=b\"$
\n" ); document.write( "Plugging this result into the previous equation gives:
\n" ); document.write( " $\"2m=-2\"$ , or $\"m=-1\"$ \r
\n" ); document.write( "\n" ); document.write( "Now, we plug our solution for m and b back into the line equation. So the equation of the line through the two points is: $\"highlight%28y=-x%2B2%29\"$ .\r
\n" ); document.write( "\n" ); document.write( "As you will see from the graph of $\"y=-x%2B2\"$ , the line goes through both of the points.
\n" ); document.write( " $\"graph%28300%2C200%2C-5%2C5%2C-5%2C5%2C-x%2B2%29\"$
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