4A

Graphing straight lines

Sketching lines using the x- and y-intercepts, lines through the origin, and horizontal and vertical lines.

The intercept method

Example 1●

Sketch $3x + 2y = 12$.

$x = 0$: $2y = 12$, so $y = 6$.

$y = 0$: $3x = 12$, so $x = 4$.

Join $(0, 6)$ and $(4, 0)$.

Lines of the form ax + by = c

Change a, b and c and watch the intercepts move.

Lines with one intercept

$y = mx$ passes through the origin; find a second point by substituting, e.g. $x = 1$.
$y = k$ is horizontal; $x = h$ is vertical.

Flashcards

$y$-intercept

Set $x = 0$.

$y = -2$

Horizontal line

$y = 4x$

Through the origin

Practice

For $3x + 2y = 12$, give the $x$-intercept then the $y$-intercept.
For $2x - 5y = 10$, give the $x$-intercept then the $y$-intercept.
The line $x = -2$ is:
Which line passes through the origin?
Find the $y$-intercept of $y = 3 - 2x$.
Find the $x$-intercept of $y = 3 - 2x$.
For $x + 4y = 8$, find the $x$-intercept.
Where do $y = 4$ and $x = -1$ meet?

More questions

New numbers every time. Keep going until you get five in a row.