1. anonymous

Two graphs are shown below: graph A shows scatter points 1, 3 and 2, 5 and 3, 7 and 4, 9 and 5, 11graph A shows scatter points 1, 11 and 2, 9 and 3, 7 and 4, 5 and 5, 3 Which scatter plot shows a linear relationship between x and y? Only graph A Only graph B Both graph A and graph B Neither graph A nor graph B

2. anonymous

Here is the graph: http://prntscr.com/88hmnm

3. SolomonZelman

You can see if the points have a pattern (x,y) $$\Longrightarrow$$ (x+a)(y+b)

4. SolomonZelman

(1,3) $$\Longrightarrow$$ (1+$$\color{red}{1}$$)(3+$$\color{blue}{2}$$)=(2,5) (2,5) $$\Longrightarrow$$ (2+$$\color{red}{1}$$)(5+$$\color{blue}{2}$$)=(3,7) (3,7) $$\Longrightarrow$$ (3+$$\color{red}{1}$$)(7+$$\color{blue}{2}$$)=(4,9) agree that this is the pattern here?

5. anonymous

1,2?

6. SolomonZelman

What do you mean?

7. SolomonZelman

So we have showed that the pattern here is indeed: (x,y) $$\Longrightarrow$$ (x+$$\color{red}{1}$$)(y+$$\color{blue}{2}$$) So each time you are adding 1 to the x, you are adding 2 to the y. (Saying as the grph goes $$\color{red}{1}$$ unit right, it goes $$\color{blue}{2}$$ units up) (lets call change in x, $$\Delta x$$ AND lets call change in y, $$\Delta y$$ ) $${\rm m}~=~\dfrac{\Delta y}{\Delta x}=\dfrac{\color{blue}{2}}{\color{red}{1}}=\bf 2$$ So the set of point A, is a line with a slope of 2:)