document.write( "Question 1025978: 7. Consider the line L represented by the equation x + 4y = 12. (a) Find the equation of the line which is parallel to L, and passes through (1,−2). (b) Find the equation of the line which is perpendicular to L, and passes through (0,1). (c) Find the intersection point of L and the line 2x−3y + 9 = 0 (d) Find the perpendicular distance from the point P(−1.5) to \n" ); document.write( "
Algebra.Com's Answer #641250 by Cromlix(4381)\"\" \"About 
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Hi there,
\n" ); document.write( "a) Sort equation into y = mx + c form.
\n" ); document.write( "x + 4y = 12
\n" ); document.write( "4y = -x + 12
\n" ); document.write( "y = -1/4x + 3
\n" ); document.write( "Gradient (Slope) = -1/4
\n" ); document.write( "Lines that are parallel have the
\n" ); document.write( "same gradient.
\n" ); document.write( "m1 = m2
\n" ); document.write( "Using line equation
\n" ); document.write( "y - b = m(x - a)
\n" ); document.write( "m = -1/4 (a,b) = 1,-2)
\n" ); document.write( "y - (-2) =-1/4(x - 1)
\n" ); document.write( "y + 2 = -1/4x + 1/4
\n" ); document.write( "y = -1/4x + 1/4 - 8/4 (2)
\n" ); document.write( "y = -1/4x - 7/4
\n" ); document.write( "b) Lines that are perpendicular to
\n" ); document.write( "one another have gradients that
\n" ); document.write( "multiply together to give -1
\n" ); document.write( "m1 x m2 = -1
\n" ); document.write( "-1/4 x m2 = -1
\n" ); document.write( "m2 = 4
\n" ); document.write( "Using line equation
\n" ); document.write( "y - b = m(x - a)
\n" ); document.write( "m = 4 (a,b) = (0,1)
\n" ); document.write( "y - 1) = 4(x - 0)
\n" ); document.write( "y - 1 = 4x
\n" ); document.write( "y = 4x + 1
\n" ); document.write( "c)Simultaneous equation:
\n" ); document.write( "x + 4y = 12......(1)
\n" ); document.write( "2x - 3y = -9.....(2)
\n" ); document.write( "Multiply Eq(1) by 2
\n" ); document.write( "2x + 8y = 24......(1)
\n" ); document.write( "2x - 3y = -9......(2)
\n" ); document.write( "Subtract Eq(2) from Eq(1)
\n" ); document.write( "11y = 33
\n" ); document.write( "y = 3
\n" ); document.write( "Substitute y = 3
\n" ); document.write( "into Eq(2)
\n" ); document.write( "2x - 3y = -9
\n" ); document.write( "2x - 3(3) = -9
\n" ); document.write( "2x - 9 = -9
\n" ); document.write( "2x = -9 + 9
\n" ); document.write( "2x = 0
\n" ); document.write( "x = 0
\n" ); document.write( "{0.3} Intersection point.
\n" ); document.write( "d) not sure what the other point
\n" ); document.write( "was as it was cut off.
\n" ); document.write( "Assuming the intersection point.
\n" ); document.write( "(0,3) and P(-1,5)
\n" ); document.write( "Formula:
\n" ); document.write( "√(x2 - x1)^2 + (y^2 - y^1)^2
\n" ); document.write( "√(-1 - 0)^2 + (5 - 3)^2
\n" ); document.write( "√ 1 + 4
\n" ); document.write( "= √5
\n" ); document.write( "= 2.236 units
\n" ); document.write( "Hope this helps :-) \n" ); document.write( "
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