Parallel lines questions with answers

Questions

1. Question 1Gradient of a parallel line

   Write down the gradient of a line parallel to $x + 2y = 3$.

   Show the worked solution

   1. Step 1: Make y the subject$y = -\dfrac{1}{2}x + \dfrac{3}{2}$
   2. Step 2: Parallel lines have the same gradientGradient $= -\dfrac{1}{2}$
2. Question 2Parallel line through a point

   Find the equation of the line parallel to $y = -2x + 4$ that passes through $(-2, 5)$.

   Show the worked solution

   1. Step 1: Same gradient as the given line$m = -2$
   2. Step 2: Substitute the point to find c$5 = -2(-2) + c$$c = 1$
   3. Step 3: Write the equation$y = -2x + 1$
3. Question 3Find k for parallel lines

   The lines $kx + 4y = 5$ and $y = 3x + 1$ are parallel. Find $k$.

   Show the worked solution

   1. Step 1: Parallel lines have the same gradient$4y = -kx + 5$, so the gradient is $-\dfrac{k}{4}$$-\dfrac{k}{4} = 3$
   2. Step 2: Solve for k$k = -12$
4. Question 4Parallel to ax + by = c

   Find the equation of the line parallel to $2x + y = -4$ that passes through $(-2, -3)$.

   Show the worked solution

   1. Step 1: Same gradient as the given line$m = -2$
   2. Step 2: Substitute the point to find c$-3 = -2(-2) + c$$c = -7$
   3. Step 3: Write the equation$y = -2x - 7$