document.write( "Question 1025982: 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 L \n" ); document.write( "
Algebra.Com's Answer #641309 by Boreal(15235)\"\" \"About 
You can put this solution on YOUR website!
x+4y=12
\n" ); document.write( "4y=-x+12
\n" ); document.write( "y=(-x/4)+3
\n" ); document.write( "parallel to this and passing through (1,-2)
\n" ); document.write( "point slope formula with slope (-1/4)
\n" ); document.write( "y+2=(-1/4)(x-1)
\n" ); document.write( "y=(-x/4)-(7/4)
\n" ); document.write( "\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C%28-x%2F4%29%2B3%2C%28-x%2F4%29-%287%2F4%29%29\" THIS IS PARALLEL
\n" ); document.write( "Perpendicular has slope 4, negative reciprocal.
\n" ); document.write( "passing through (0,1) y-1=4x; y=4x+1.
\n" ); document.write( "\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C%28-x%2F4%29%2B3%2C4x%2B1%29\"THIS IS PERPENDICULAR
\n" ); document.write( "X+4Y=12
\n" ); document.write( "2X-3Y=-9, rewriting
\n" ); document.write( "-2X-8Y=-24, multiplying top by -2.
\n" ); document.write( "-11Y=-33
\n" ); document.write( "Y=3
\n" ); document.write( "X=0 (0,3) IS THE INTERSECTION POINT.
\n" ); document.write( "From (-1,5) to L, the perpendicular distance must be along a line with slope 4
\n" ); document.write( "that line has an equation of y-5=4(x+1); y-5=4x+4 and y=4x+9
\n" ); document.write( "Find the intersection of that line and the original line
\n" ); document.write( "x+4y=12
\n" ); document.write( "-4x+y=9
\n" ); document.write( "4x+16y=48 multiplying the first by 4.
\n" ); document.write( "17y=57; y=57/17
\n" ); document.write( "x+4y=12
\n" ); document.write( "16x-4y=-36
\n" ); document.write( "17x=-24; x=-24/17
\n" ); document.write( "Do those points work in both lines?
\n" ); document.write( "-24/17 +228/17=204/17, which is 12.
\n" ); document.write( "y=4x+9 or 57/17=4(-24/17)+153/17. This is (-96+153)/17=57/17.
\n" ); document.write( "Therefore, the intersection is (-24/17, 57/17) and we need to find the distance between that point at (-1.5)
\n" ); document.write( "That is the distance formula, with is the square root (sum of the square of the distances of x and y).
\n" ); document.write( "x distance is from -1 to -24/17, which is -7/17. y distance is between 5 and 57/17, and that is (28/17).
\n" ); document.write( "Square those and add them, which is (49/289) and (784/289) or (833/289). The square root of that is sqrt(833)/17=28.86/17, or 1.698 or 1.7
\n" ); document.write( "\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C%28-x%2F4%29%2B3%2C+4x%2B9%29\" \n" ); document.write( "
\n" );