Finding the rule

Finding a linear rule from a table of values or a pattern by using the constant difference and the value when x = 0.

From a table

Example 1●

Find the rule: $x = 0, 1, 2, 3$ gives $y = 4, 7, 10, 13$.

$y$ goes up by $3$, so $m = 3$. At $x = 0$, $y = 4$.

$y = 3x + 4$

Example 2●●

Find the rule: $x = 1, 2, 3, 4$ gives $y = 1, -1, -3, -5$.

$y$ goes down by $2$, so $m = -2$.

Working back to $x = 0$: $y = 1 + 2 = 3$. So $y = -2x + 3$.

Flashcards

Constant difference

The gradient $m$

Value at $x = 0$

The $y$-intercept $c$

$x$: 0,1,2; $y$: 5,7,9

$y = 2x + 5$

Practice

$x = 0, 1, 2, 3$ gives $y = 4, 7, 10, 13$. Find the rule: $y = $ ?
$x = 1, 2, 3, 4$ gives $y = 1, -1, -3, -5$. Find $y = $ ?
$x = 0, 1, 2$ gives $y = 5, 7, 9$. Find $y = $ ?
$x = 1, 2, 3$ gives $y = 3, 7, 11$. Find $y = $ ?
Using $y = 3x + 4$, find $y$ when $x = 9$.
$x = 1, 2, 3$ gives $y = 5, 10, 15$. Find $y = $ ?
$x = 0, 1, 2$ gives $y = 10, 9, 8$. Find $y = $ ?
Matchstick pattern: shape $n = 1, 2, 3$ uses $3, 5, 7$ sticks. Find the rule for the number of sticks in terms of $n$.