Parallel Lines Flashcards

All 6 cards in this deck

What is true about the gradients of two parallel lines?

They are equal.

What are the steps to show that two lines are parallel?
e.g. $y = 2x + 3$ and $5y - 10x + 4 = 0$

1. Rearrange each into $y = mx + c$: $y = 2x - \frac{4}{5}$
2. Compare the gradients: both are $2$
3. State: same gradient, so the lines are parallel

Write down the equation of a straight line parallel to $y = 5x$.

$y = 5x + c$ for any $c \neq 0$, e.g. $y = 5x + 2$.

True or false? Two lines that cross the $y$-axis at the same point are parallel.

False. Parallel lines need equal gradients; lines sharing a $y$-intercept cross there unless they are the same line.

True or false? $y = 3x + 1$ and $y = 3x - 7$ are parallel.

True. Both have gradient $3$ and different $y$-intercepts.

True or false? You can compare the gradients of $y = \frac{1}{2}x - 6$ and $6y = 3x + 7$ straight away, without rearranging.

False. The second must be written as $y = mx + c$ first, giving $y = \frac{1}{2}x + \frac{7}{6}$.