LINEAR LAW. Draw the line of best fit 3 4 log log. Write the equation for the line of best fit of the following graphs.. P(,3). Q(6,3).. P(,5) Q(,). [ 5 3 3 [ 5 5 Linear law
3. P(-,4). Q(5,6) 4. P(,8). Q(3,) 5 [= +6 s B(5,9) A(3,) t 6 [=-3 + P. A(-,5). B(4,) V 7 [ 9 7 s t p B(5,3) 8 [ P v 4 P A(,) A(, ) q. B(3, ) V [ p = 5 7 q 6 6 [ 3 p v 5 Linear law
.3 Determine the values of variables from lines of best fit The diagram below shows a line of best fit. From the graph, find The diagram below shows a line of best fit. From the graph, find i. the value of when =.5 i. the value of t when w = 38 ii. the value of when = 7 ii. the value of w when t =.6 8 6 4 W 4 3 3 4 3 4 t [.8, 3.3 3 The diagram below shows a line of best fit obtained b plotting the graph of d against t. The line intersects the vertical and the horizontal aes at points (,) and (6,) respectivel. Find i. the equation of best fit ii. the value of t when d=3 iii. the value of d when t=4 d (,) [3.6, 4 Two variables, p and q are known to be linearl related as shown b the line of best fit in the diagram below. The line passes through points (.6, 6) and (3.6, 3). Determine i. the equation of best fit ii. the value of q when p= 5 iii. the value of p when q = 5 p (3, 3) (6,) t (, 6) q [ d t, 3, 3 3 [p=q+4, 5.5, 4 Linear law 3
. Reduce non linear relations to linear form Reduce each of the equations to the form Y=m +C where a and b are constants. Non-linear equation Linear equation Y m C = a + b B = a 3 + b a b 3 a = b 4 a = b 5 = a b 6 +b = a 7 5 3 8 a( b ) 9 = ab log b A 5 = a b log a =a b b PV=a P. Determine values of constants of non-linear relations given lines of best fit The diagram below shows the line of best fit for the graph of against. Determine the non-linear equation connecting and. P(,4) The diagram below shows the line of best fit for the graph of against. Determine the non-linear equation connecting and. Q(,) Q(,) P(,) [ =-+4 [ 5 Linear law 4
3 The diagram below shows the line of best fit for the graph of against. Determine the non-linear equation connecting and. P(3,) Q(6,) 4 The diagram below shows the line of best fit for the graph of against. Determine the non-linear equation connecting and. (4, 5) (,4) [ 4 5 The diagram below shows the line of best fit for the graph of log against. Determine the non-linear equation connecting and. log (,6) [ 3 6 The diagram below shows the line of best fit for the graph of log against log. Determine the non-linear equation connecting and. log (,6) (,) (,) log [log = 3 [ log = log + Linear law 5
7 The diagram below shows the line of best fit for the graph of against. Determine the relation between and. 8 The diagram below shows the straight line graph of against. Epress in terms of. Q(4,) (4,) P(,4) (, ) 4 [ 4 9 The diagram below shows the straight line graph of against. Epress in terms of. [ 3 The diagram below shows the line of best fit for the graph of against. Determine the relation between and. (4,) Q(4,) (, ) P(,4) [ 3 4 4 [ Linear law 6
The diagram below shows the line when against is drawn. Epress as a function of. 3 The diagram below shows the line when against is drawn. Epress as a function of. 5 (8, -3) (, -) 3 [ 3 4 3 The diagram below shows the line of best fit for the graph of against. Determine the relation between and. P(3,) Q(6,) [ 5 4 The diagram below shows the line when against is drawn. Epress as a function of. (4, 5) (,4) 3 [ 4 [ 3 3 Linear law 7
5 The diagram below shows the line when against is drawn. Epress in terms of. (,8) 6 The diagram below shows the line when against is drawn. Determine the non-linear equation connecting and (8,) (-4,) (4,) [= +8-7 The diagram below shows the line when against is drawn. Determine the non-linear equation connecting and (3,6) [ 6 8 The diagram below shows the line of best fit for the graph of log against. Determine the relation between and. log (,6) (,3) (,) [ 3 9 The diagram below shows part the graph of log against. Form the equation that connecting and. log [ = 3 The diagram below shows the line of best fit for the graph of log against log. Determine the relation between and. log (3,4) (4,) (,) (,6) log 4 6 [ [= Linear law 8
The diagram below shows part the graph of log against log. Form the equation that connecting and. log -3 6 log The diagram below shows part the graph of log against log. Determine the relation between and. log (5,6) log [ 3 SPM 3 Paper Q and are related b the equation p q, where p and q are constants. A straight line is obtained b plotting the diagram below. (,9) against, as shown in (6,) [ 6 4 SPM 4 Paper Q3 Diagram below shows a straight line graph of against (, k) (h, 3) Given that = 6-, calculate the value of k and h [3 marks Calculate the values of p and q. [4 marks [p= -, q =3 [h=3, k=4 Linear law 9
5 SPM 5 Paper Question 3 The variables and are related b the equation =k 4, where k is a constant. (a) Convert the equation =k 4 to linear form. (b) Diagram below shows the straight line obtained b plotting log against log log (, h ) 6 The diagram below shows a straight line graph log against. The variables and are related b the equation = ab, where a and b are constants. Find the values of (i) a (ii) b log (3, 7 ) (, 3) log Find the value of (i) log k (ii) h [4 marks (, ) [3, [,.3 Obtain information from (i) lines of best fit (ii) equations of lines of best fit.. Use graph paper to answer this question. The table below records the values of an eperiment for two variables and which are related b q p where p and q are constants..8.3.4.5.7 8.75 79 45.38 36.5 6.67 8.9 (a) Plot against 3 using scale cm represents unit in -ais and cm represents units for -ais. Hence, draw the line of best fit [5marks (b) From the graph, estimate the value of (i) p and q 45 (ii) when = [5marks [Answer:p=-6.67, q=95, =.458 Linear law
. Use graph paper to answer this question. The table below records the values of an eperiment for two variables and which are related b where p and k are constants. p k 3 5 6 7 8 9 4.7 4. 3.6 3..5.8 (a) Plot the graph against [4 marks (b) use the graph to estimate the values of (i) p (ii) k. (iii) which satisf the simultaneous equation p k and = [6 marks [answer: p=5, k= -.4, = 8.6-8.75 3. Use graph paper to answer this question. The table below records the values of an eperiment for two variables and which are related b Y=pq where p and q are constants. 3 4 5 6 7 5 4 8 (a) Plot the graph log against [4 marks (b) Use the graph to estimate the values of (i) p (ii) q. (iii) when =4.8 [6 marks [answer:.995,.666, 7.38 4. SPM 3 Paper Question 7 Use graph paper to answer this question. Table below shows the value of two variables, and, obtained from an eperiment. It is known that and are related b the equation pk,where p and k are constants.5..5 3. 3.5 4..59.86.4 3.7 4.36 6.76 (a) Plot log against Hence, draw the line of best fit. (b) Use the graph in (a) to find the value of (i) p (ii) k [5 marks [5 marks [ Answer: p=.59, k =.9 Linear law
5. SPM 4 Paper Question 7 Use graph paper to answer this question. Table below shows the values of two variables, and, obatained from an eperiment. Variables and are related b the equation = p k, where p and k are constants. 4 6 8 3.6 5.5 5.5 6. 8.84 46.77 (a) Plot log against b using a scale of cm to units on the -ais and cm to. unit on the log -ais. Hence, draw the line of best fit [4 marks (b) Use our graph from (a) to find the value of (i) p (ii) k [ 6 marks Answer :p =.8, k =.39 6. SPM 5 Paper Question 7 Use graph paper to answer this question. Table below shows the values of two variables, and, obtained from eperiment. The variables and are r related b the equation p, where p and r are constants. p.. 3. 4. 5. 5.5 5.5 4.7 5. 6.5 7.7 8.4 (a) Plot against, b using a scale of cm to 5 units on both aes. Hence, draw the line of best fit. (b) Use the graph from (a) to find the value of (i) p (ii) r Answer :[ p=.37, r=5.48 [5 marks [5 marks 7. SPM 6 Paper Question 7 Use graph paper to answer this question. Table below shows the values of two variables, and, obtained from an eperiment. Variables and are related b the equation pk, where p and k are constants. 3 4 5 6 4. 5.7 8.7 3.. 8.8 (a) Plot log against (+), using a scale of cm to unit on the (+) ais and cm to. unit on the log -ais. Hence, draw the line of best fit. [5 marks (b) Use ou graph from (a) to find the values of (i) p (ii) k [5 marks Linear law
Answer for. Non-linear equation Linear equation Y m C = a + b a b a b = a 3 + b a b a b 3 = b a b a b a 4 = b a b a a b 5 b = a b a b( ) a 6 +b = a b a 7 5 3 3 5 8 a( b ) ( ab) a log (log b) log a -b a -3 5 ab -a 9 = ab log log b log a = a b log log b log a log b(log ) log a =a b log b(log ) log a log log b log a PV=a a P V P V a Linear law 3