perpendicular/parallel to another line. Line (L) has the equation X+2y=5 A) Write the equation of a line parallel to (L) that passes through the point (-1,2) B) Write the equation of a line perpendicular to (L) that passes through the point (-1,2)
Slope = -1/2 A ) There is a couple different ways to do this, point slope form: y - 2 = -1/2(x + 1) y - 2 = -1/2x + 0.5 y = -1/2x + 2.5 For the second problem, i forget how to do perpendicular :-/
first, solve first equation for y: y=(-1/2)x+5 slope of this line is -1/2. parallel lines have identical slopes, so any line with same slope will do. But your line needs to pass through -1,2 so plug these in for the x and y variables and solve for the y intercept. ex. 2=(-1/2)*-1+b 2-b=(-1/2)*-1 2-b=1/2 -b=(1/2)-2 b=3/2 then plug into original equation again: y=(-1/2)x+(3/2) perpendicular lines have negative inverse slopes. the negative inverse of -1/2 is 2, so any line with a slope of 2 will do. But your line needs to pass through -1,2 so plug these in for the x and y variables and solve for the y intercept. ex. 2=2*-1+b 2-b=-2 -b=-4 b=4 then plug into original equation again: y=2x+4 Hope that helps
Original Equation: y=-1/2x+5/2 Parallel: y=-1/2x+3/2 Perp: y=2x+4 The way to find parallel is to solve the original equation and get the slope (-1/2) and then plug in for M into the equation: (y-y1)=Mx(x-x1) then just plug in the points (x1,y1) (in this case its (-1,2)) and solve. For Perp, it is the same thing, but you flip your original slope and change the sign.
Remember parallel lines have identical slopes and perpendicular lines have opposite reciprocal slopes (meaning opposite sign and flip the fraction). Opposite Reciprocal Example: 1/3 -> -3 6/7 -> -7/6 -7 -> 1/7 Hope that helps .