# What is the function rule for these ordered pairs (-2, 10) (-1, -7) (0, -4) (1, -1) (2, 2)?

May 30, 2016

$\textcolor{b l u e}{\text{So the function rule is } y = 3 x - 4}$

#### Explanation:

Given:
y-> 10;-7;-4;-1;2
x->-2;-1;0;1;2
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Assumption: the question has an error. The +10 should be -10

Thus we have

${y}_{2} - {y}_{1} \to - 7 - \left(- 10\right) = + 10 - 7 = + 3$

$\text{-10 -7 -4 -1 2}$
$\text{ \/"color(white)(.)"\ /"color(white)(.)"\/"color(white)(.)"\/}$
$\text{ 3 3 3 3 " larr " difference in "y" (increasing)}$

$\text{-2 -1 0 1 2}$
$\text{ \/"color(white)(.)"\ /"color(white)(.)"\/"color(white)(.)"\/}$
" 1 1 1 1 " larr " difference in "x" (increasing")

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Consider the standard form equation of a straight line:
$\text{ } y = m x + c$

where m is the gradient $\to \left(\text{change in y")/("change in x}\right) \to \frac{+ 3}{+ 1} = + 3$

$y = 3 x + c$

Take any given point $P \to \left(x , y\right) \text{ } \to \left(- 1 , - 7\right)$

Then $y = 3 x + c \text{ " ->" } - 7 = 3 \left(- 1\right) + c$

$\implies c = 3 - 7 = - 4$
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$\textcolor{b l u e}{\text{So the function rule is } y = 3 x - 4}$ 