Intercepts and graphical solutions

Finding the x- and y-intercepts of a line, sketching with intercepts, and solving equations or pairs of equations from where lines meet.

Intercepts

Example 1●

Find the intercepts of $y = 2x - 6$.

$x = 0$: $y = -6$.

$y = 0$: $2x = 6$, so $x = 3$.

Point of intersection

The meeting point satisfies both equations at once.

Example 2●●

Where do $y = x + 1$ and $y = -x + 5$ meet?

$x + 1 = -x + 5$, so $2x = 4$ and $x = 2$.

$y = 3$. They meet at $(2, 3)$.

Flashcards

$y$-intercept

Set $x = 0$.

$x$-intercept

Set $y = 0$.

Where two lines meet

The point that satisfies both equations.

Practice