Parallel Lines Flashcards

All 5 cards in this deck

How can you tell from their equations that two straight lines are parallel?

They have the same gradient (the same value of $m$ in $y = mx + c$) but different values of $c$.

e.g. $y = 3x - 2$ and $y = 3x + 5$

What are the steps to show that two lines are parallel when one is not in the form $y = mx + c$?

e.g. $y = 3x - 2$ and $3y - 9x + 5 = 0$

1. Rearrange into $y = mx + c$: $3y = 9x - 5$, so $y = 3x - \frac{5}{3}$
2. Compare the coefficients of $x$: both are $3$
3. State the conclusion: both lines have gradient $3$, so they are parallel

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

Any line $y = 5x + c$ with $c \neq 0$.

e.g. $y = 5x + 2$

True or false? The lines $y = 2x + 1$ and $y = 3x + 1$ are parallel.

False.

Their gradients differ ($2$ and $3$); they both pass through $(0, 1)$, so they cross there.

True or false? Two different parallel lines can have the same $y$-intercept.

False.

Same gradient and same $y$-intercept means they are the same line.