if a linear relationship exists define a formula relating th

if a linear relationship exists, define a formula relating the two quantities.

Which of these relatiotalups could be linear? Seleot all thet epply t a lner relationship exists between Nand N a linear relationship exists between ul and e IE n liner relntiotslup exists, detine a fonda relning the two qreentitics. If ftle relatiousluip is not linear wri DNE Preview s Preview

Solution

Note: Variable names are not vsisble in each data, so suitable varibale names have been assumed.

Realtionship is linear if rate of change of quatity remains same i.e. ( y2-y1)/(x2-x1) = constant

Ist data Table is linear because the k value remains change and the rate of change of k and N remains zero

formul relating the quantities can be defined as k = -3.4

IInd data Table is a linear relationship because the rate of change of quantities ( d2-d1)/(m2-m1) remains constant

Rate of change between any set of values =-10.

Selecting one point ( m,d) = ( -0.4, 13.9) to find the formula relating the quantities:

d = -10m +c ---> 13.9 = -0.4*-10 +c ---> c= 9.9

d = -10m + 9.9

IInd data Table is a linear relationship because the rate of change of quantities ( e2-e1)/(w2-w1) remains constant

Rate of change between any set of values = -3.3

Selecting one point (w,e) = (0.5, -1.75) to find the formula relating the quantities:

e = -3.3w +c ----> -1.75 = -3.3*0.5 +c ----> c= -0.1

e = -3.3w -0.1