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I can't exactly figure out how to work this out.

Well I know the equation for a straight line is $y = mx + c$

$c = gradient$

Therefore if I multiply $3$ by the number $x$ to get the gradient $6$ and $2$ I can work out which is line is which...

With $y = 3(x + 2)$ I tried to expand but then I got confused.

Can someone explain in easy terms? Thanks guys.

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3 Answers 3

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Do you know the distributive property? a(b+c)=ab+ac

If you can write in slope-intercept form...that is y=mx+b..you can determine the y-intercept is b since when x=0 y=b.

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It seems your main trouble is expanding the equation $$y= 3(x+2)$$ The distributive property goes as follows, $$a(b+c) = a\cdot b + a\cdot c$$ Thus, $$3(x+2) = 3x + (3 \cdot 2) = 3x+6$$ In this equation the 3 represents the slope and the 6 represents the y-intercept. You should now be able to correctly identify which line is which.

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Syntactical side note: $m$ is called the gradient, $c$ is called the $y$-intercept.
To find the correct equation for $A$, just look at the $y$-intercept of $A$: it's $6$.

This means that $A$ must be of the form $y = mx + 6$, wich only one of your equations satisfies. Note that

$$a\cdot(b+c) = a\cdot b + a\cdot c$$ for any real numbers (also variables) $a,b$ and $c$.

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