document.write( "Question 150744: what is the equation in the standard form of the line through (4,1) and (-2,3)? \n" ); document.write( "

Algebra.Com's Answer #110669 by Electrified_Levi(103) $\"\"$ $\"About$

You can put this solution on YOUR website!
Hi, Hope I can help,
\n" ); document.write( ".
\n" ); document.write( "what is the equation in the standard form of the line through (4,1) and (-2,3)?
\n" ); document.write( ".
\n" ); document.write( "First, we need to find the slope of the line.
\n" ); document.write( ".
\n" ); document.write( "We can find the slope by using the two points ( the slope is equal to $\"+%28y2+-+y1%29%2F%28x2+-+x1%29+\"$ or $\"+%28y1+-+y2%29%2F+%28x1+-+x2%29+\"$
\n" ); document.write( ".
\n" ); document.write( "We will use the first equation
\n" ); document.write( ".
\n" ); document.write( "(4,1)( x1 , y1 ) and (-2,3) ( x2 , y2 )
\n" ); document.write( ".
\n" ); document.write( " $\"+%28y2+-+y1%29%2F%28x2+-+x1%29+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+%283+-+1%29+%2F+%28%28-2%29+-+4+%29+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+2%2F+%28-6%29+\"$
\n" ); document.write( ".
\n" ); document.write( "It will reduce to $\"+%28-1%29%2F3+\"$
\n" ); document.write( ".
\n" ); document.write( " - $\"+1%2F3+\"$ is the slope
\n" ); document.write( ".
\n" ); document.write( "The slope intercept form of a line = $\"+y+=+mx+%2B+b+\"$ m = slope, b = unknown
\n" ); document.write( ".
\n" ); document.write( "We can replace \"m\" with - $\"+1%2F3+\"$
\n" ); document.write( ".
\n" ); document.write( "It becomes $\"+y+=+%28-1%2F3%29x+%2B+b+\"$
\n" ); document.write( ".
\n" ); document.write( "We can find \"b\" by replacing \"x\" and \"y\" with one of our points
\n" ); document.write( ".
\n" ); document.write( "(4,1)(x,y) and (-2,3) (x,y)
\n" ); document.write( ".
\n" ); document.write( "We will use the first point, (4,1) (x,y)
\n" ); document.write( ".
\n" ); document.write( " $\"+y+=+%28-1%2F3%29x+%2B+b+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+%281%29+=+%28-1%2F3%29%284%29+%2B+b+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+1+=+%28-4%2F3%29+%2B+b+\"$
\n" ); document.write( ".
\n" ); document.write( "We will move $\"+%28-4%2F3%29+\"$ to the left
\n" ); document.write( ".
\n" ); document.write( " $\"+1+%2B+%284%2F3%29+=+%28-4%2F3%29+%2B+%284%2F3%29+%2B+b+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+%287%2F3%29+=++b+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+b+=+%287%2F3%29+\"$
\n" ); document.write( ".
\n" ); document.write( "We can replace \"b\" with $\"+7%2F3+\"$ in our equation
\n" ); document.write( ".
\n" ); document.write( " $\"+y+=+%28-1%2F3%29x+%2B+b+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+y+=+%28-1%2F3%29x+%2B+%287%2F3%29+\"$
\n" ); document.write( ".
\n" ); document.write( "That is the slope intercept form of the equation, The standard form is $\"+Ax+%2B+By+=+C+\"$
\n" ); document.write( ".
\n" ); document.write( "To get it to the standard form, we need to get rid of the fractions
\n" ); document.write( ".
\n" ); document.write( " $\"+y+=+%28-1%2F3%29x+%2B+%287%2F3%29+\"$
\n" ); document.write( ".
\n" ); document.write( "We will multiply everything by \"3\"
\n" ); document.write( ".
\n" ); document.write( " $\"+%283%29y+=+%283%29%28-1%2F3%29x+%2B+%283%29%287%2F3%29+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+3y+=+%28-1%29x+%2B+7+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+3y+=+%28-x%29+%2B+7+\"$
\n" ); document.write( ".
\n" ); document.write( "We will move (-x) to the left side
\n" ); document.write( ".
\n" ); document.write( " $\"+3y+%2B+x+=+%28-x%29+%2B+x+%2B+7+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+3y+%2B+x+=+7+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+x+%2B+3y+=+7+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+x+%2B+3y+=+7+\"$ is the standard form,
\n" ); document.write( ".
\n" ); document.write( " $\"+Ax+%2B+By+=+C+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+%281%29x+%2B+%283%29y+=+%287%29+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+x+%2B+3y+=+7+\"$
\n" ); document.write( ".
\n" ); document.write( "We can check by replacing \"x\" and \"y\" with the two points
\n" ); document.write( ".
\n" ); document.write( "(4,1) and (-2,3)
\n" ); document.write( ".
\n" ); document.write( "We will use the first point, (4,1) (x,y)
\n" ); document.write( ".
\n" ); document.write( " $\"+x+%2B+3y+=+7+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+4+%2B+3%281%29+=+7+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+4+%2B+3+=+7+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+7+=+7+\"$ True
\n" ); document.write( ".
\n" ); document.write( "We will use the second point, (-2,3) (x,y)
\n" ); document.write( ".
\n" ); document.write( " $\"+x+%2B+3y+=+7+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+%28-2%29+%2B+3%283%29+=+7+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+%28-2%29+%2B+9+=+7+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+7+=+7+\"$ True
\n" ); document.write( ".
\n" ); document.write( "Some other points to $\"+x+%2B+3y+=+7+\"$ = (1,2), (7,0), and (-8,5)
\n" ); document.write( ".
\n" ); document.write( " $\"+x+%2B+3y+=+7+\"$ is the standard equation for the line
\n" ); document.write( ".
\n" ); document.write( "Hope I helped, Levi\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );