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

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

anonymous · Answer

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.