Question

Does the table represent linear relationship? If yes, write an equation. If no, explain.

a). x:-1,0,1,2
y:0,6,12,18

b). x:0,1,2,3
y:2,4,8,16

Answer 1

a) So we have four points to work with (-1,0), (0,6),(1,12) and (2,18). Take any two points find the slope:\[slope=(6-0)/(0-(-1))=6\]If any other points are on this line the following must hold:\[y-0=6(x-(-1))\]Or,\[y=6(x+1)\]We need to check if (1,12) and (2,18) satisfy this equation:\[12=6(1+1)=12\]Yep. Last point:\[18=6(2+1)=18\]Yep again. All points are on a line; the relationship is linear with equation:\[y=6(x+1)\]Or,\[y=6x+6\]If you prefer slope-intercept form. Question b is done exactly the same way. The relationship in question b is NOT linear.