Graph the following linear function y = 1 2 x . Identify the constant of variation and verify it with the graph. Also find y when x = 9 .

Given, the linear function y = 1 2 x y = k x ∴ Constant of variation, k = 1 2 x 2 4 6 10 16 y 1 2 3 5 8 Plot the points ( 2 , 1 ) , ( 4 , 2 ) , ( 6 , 3 ) , ( 10 , 5 ) , ( 16 , 8 ) on the graph. Scale: X axis, 1 cm = 2 units and Y axis, 1 cm = 1 unit , Verifying the constant of verification from graph. Taking two points from graph, ( 6 , 3 ) and ( 10 , 5 ) Slope m = y 2 - y 1 x 2 - x 1 = 5 - 3 10 - 6 = 2 4 = 1 2 ∴ From graph constant of variation is 1 2 . Hence, from the graph when x = 9 then y = 4 . 5

Graph the following linear function y = 1 2 x . Identify the constant of variation and verify it with the graph. Also find y when x = 9 .

Given, the linear function y = 1 2 x y = k x ∴ Constant of variation, k = 1 2 x 2 4 6 10 16 y 1 2 3 5 8 Plot the points ( 2 , 1 ) , ( 4 , 2 ) , ( 6 , 3 ) , ( 10 , 5 ) , ( 16 , 8 ) on the graph. Scale: X axis, 1 cm = 2 units and Y axis, 1 cm = 1 unit , Verifying the constant of verification from graph. Taking two points from graph, ( 6 , 3 ) and ( 10 , 5 ) Slope m = y 2 - y 1 x 2 - x 1 = 5 - 3 10 - 6 = 2 4 = 1 2 ∴ From graph constant of variation is 1 2 . Hence, from the graph when x = 9 then y = 4 . 5

The following table shows the data about the number of pipes and the time taken to fill the same tank. No. of pipes ( x ) 2 3 6 9 Time taken (in min) ( y ) 45 30 15 10 Draw the graph for the above data and hence find the time taken to fill the tank when five pipes are used.

Given, No. of pipes ( x ) 2 3 6 9 Time taken (in min) ( y ) 45 30 15 10 As a x increases y decreases, therefore the given graph is an inverse variation. In indirect variation y = k x or x y = k 2 × 45 = 3 × 30 = 6 × 15 = 9 × 90 = 90 Constant of variation is 90 Equation of variation is x y = 90 Plot the point ( 2 , 45 ) , ( 3 , 30 ) , ( 6 , 15 ) , ( 9 , 10 ) on the graph and join them to get a smooth curve. Scale: X axis - 1 cm = 1 pipe and Y axis - 1 cm = 5 minutes Hence, from the graph the time taken to fill the tank when five pipes are used is 18 minutes.

The following table shows the data about the number of pipes and the time taken to fill the same tank. No. of pipes ( x ) 2 3 6 9 Time taken (in min) ( y ) 45 30 15 10 Draw the graph for the above data and hence Find the number of pipes when the time is 9 minutes.

Given, No. of pipes ( x ) 2 3 6 9 Time taken (in min) ( y ) 45 30 15 10 As a x increases y decreases, therefore the given graph is an inverse variation. In indirect variation y = k x or x y = k 2 × 45 = 3 × 30 = 6 × 15 = 9 × 90 = 90 Constant of variation is 90 Equation of variation is x y = 90 Plot the point ( 2 , 45 ) , ( 3 , 30 ) , ( 6 , 15 ) , ( 9 , 10 ) on the graph and join them to get a smooth curve. Scale: X axis - 1 cm = 1 pipe and Y axis - 1 cm = 5 minutes Hence, from the graph the number of pipes used are 10 when the time is 9 minutes.

A school announces that for a certain competitions, the cash price will be distributed for all the participants equally as show below. No. of participants ( x ) 2 4 6 8 10 Amount for each participant in ₹ ( y ) 180 90 60 45 36 Find the constant of variation.

Given, A school announces that for a certain competitions, the cash price will be distributed for all the participants equally as show below. No. of participants ( x ) 2 4 6 8 10 Amount for each participant in ₹ ( y ) 180 90 60 45 36 We have to find the constant of variation. As x increases y decreases, therefore the given variation is an inverse variation. ∴ Equation of curve is x y = k or y = k x 2 × 180 = k , 4 × 90 = k , 6 × 60 = k , 8 × 45 = k , 10 × 36 = k ∴ Constant of variation is k = 360

A school announces that for a certain competitions, the cash price will be distributed for all the participants equally as show below. No. of participants ( x ) 2 4 6 8 10 Amount for each participant in ₹ ( y ) 180 90 60 45 36 Graph the above data and hence, find how much will each participant get if the number of participants are 12 .

Given, A school announces that for a certain competitions, the cash price will be distributed for all the participants equally as shown below. No. of participants ( x ) 2 4 6 8 10 Amount for each participant in ₹ ( y ) 180 90 60 45 36 We have to draw the graph and find how much will each participant get if the number of participants are 12 As x increases y decreases, therefore the given variation is an inverse variation. ∴ Equation of curve is x y = k or y = k x 2 × 180 = k , 4 × 90 = k , 6 × 60 = k , 8 × 45 = k , 10 × 36 = k ∴ Constant of variation is k = 360 Plot the points ( 2 , 180 ) , ( 4 , 90 ) , ( 6 , 60 ) , ( 8 , 45 ) , ( 10 , 36 ) on the graph and join them to get a smooth curve. Scale: X axis - 1 cm = 1 paticipant , Y axis - 1 cm = Rs . 10 Therefore, From the graph when the number of participants are 12 each will get Rs . 30

Connect the graphs to their respective number of points of intersection with X -axis and to their corresponding nature of solutions which is given in the following table. S.No. Graphs Number of points of intersection with X -axis Nature of solutions 1 . 2 Real and equal roots 2 . 1 No real roots 3 . 2 No real roots 4 . 0 Real and equal roots 5 . 0 Real and unequal roots 6 . 1 Real and unequal roots

We have connected the graphs to its respective number of points of intersection with x -axis and to its corresponding nature of solutions shown in the following table. S.No. Graphs Number of points of intersection with X -axis Nature of solutions 1 . 0 No real roots 2 . 2 Real and unequal roots 3 . 0 No real roots 4 . 1 Real and equal roots 5 . 2 Real and unequal roots 6 . 1 Real and equal roots Graphs- 1 & 3 are not touching with the x -axis. Thus, they have 0 roots meaning roots are not real. Graphs- 2 & 5 are intersecting at 2 different points. Thus, they have 2 roots and roots are real and unequal. Graphs- 4 & 6 are touching the x -axis at 1 point each. Thus, they have 1 root each or we can say each of them have two roots which are equal. Roots are real and equal.

EASY

10th Tamil Nadu Board

IMPORTANT

Earn 100

Graph the following linear function $y = \frac{1}{2} x$ . Identify the constant of variation and verify it with the graph. Also find $y$ when $x = 9$ .

Important Questions on Algebra

EASY

10th Tamil Nadu Board

IMPORTANT

Mathematics Standard 10>Chapter 3 - Algebra>Exercise 3.15>Q 3

Graph the following linear function

y = \frac{1}{2} x

. Identify the constant of variation and verify it with the graph. Also find

x

when

y = 7.5

EASY

10th Tamil Nadu Board

IMPORTANT

Mathematics Standard 10>Chapter 3 - Algebra>Exercise 3.15>Q 4

The following table shows the data about the number of pipes and the time taken to fill the same tank.

No. of pipes $(x)$	$2$	$3$	$6$	$9$
Time taken (in min) $(y)$	$45$	$30$	$15$	$10$

Draw the graph for the above data and hence find the time taken to fill the tank when five pipes are used.

EASY

10th Tamil Nadu Board

IMPORTANT

Mathematics Standard 10>Chapter 3 - Algebra>Exercise 3.15>Q 4

The following table shows the data about the number of pipes and the time taken to fill the same tank.

No. of pipes $(x)$	$2$	$3$	$6$	$9$
Time taken (in min) $(y)$	$45$	$30$	$15$	$10$

Draw the graph for the above data and hence Find the number of pipes when the time is $9$ minutes.

EASY

10th Tamil Nadu Board

IMPORTANT

Mathematics Standard 10>Chapter 3 - Algebra>Exercise 3.15>Q 5

A school announces that for a certain competitions, the cash price will be distributed for all the participants equally as show below.

No. of participants $(x)$	$2$	$4$	$6$	$8$	$10$
Amount for each participant in $₹$ $(y)$	$180$	$90$	$60$	$45$	$36$

Find the constant of variation.

EASY

10th Tamil Nadu Board

IMPORTANT

Mathematics Standard 10>Chapter 3 - Algebra>Exercise 3.15>Q 5

A school announces that for a certain competitions, the cash price will be distributed for all the participants equally as show below.

No. of participants $(x)$	$2$	$4$	$6$	$8$	$10$
Amount for each participant in $₹$ $(y)$	$180$	$90$	$60$	$45$	$36$

Graph the above data and hence, find how much will each participant get if the number of participants are $12$ .

EASY

10th Tamil Nadu Board

IMPORTANT

Mathematics Standard 10>Chapter 3 - Algebra>Exercise 3.15>Q 6

A two wheeler parking zone near bus stand charges as below.

Time (in hours) $(x)$	$4$	$8$	$12$	$24$
Amount $₹$ $(y)$	$60$	$120$	$180$	$360$

Check if the amount charged are in direct variation or in inverse variation to the parking time. Graph the data. Also find the amount to be paid when parking time is $6 hr$ .

EASY

10th Tamil Nadu Board

IMPORTANT

Mathematics Standard 10>Chapter 3 - Algebra>Exercise 3.15>Q 6

A two wheeler parking zone near bus stand charges as below.

Time (in hours) $(x)$	$4$	$8$	$12$	$24$
Amount $₹$ $(y)$	$60$	$120$	$180$	$360$

Check if the amount charged are in direct variation or in inverse variation to the parking time. Graph the data. Also find the parking duration when the amount paid is $₹ 150$ .

HARD

10th Tamil Nadu Board

IMPORTANT

Mathematics Standard 10>Chapter 3 - Algebra>Progress Check>Q 1

Connect the graphs to their respective number of points of intersection with $X$ -axis and to their corresponding nature of solutions which is given in the following table.

S.No.	Graphs	Number of points of intersection with $X$ -axis	Nature of solutions
$1 .$		$2$	Real and equal roots
$2 .$		$1$	No real roots
$3 .$		$2$	No real roots
$4 .$		$0$	Real and equal roots
$5 .$		$0$	Real and unequal roots
$6 .$		$1$	Real and unequal roots

Graph the following linear function y=12x. Identify the constant of variation and verify it with the graph. Also find y when x=9.

Important Questions on Algebra

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Graph the following linear function $y = \frac{1}{2} x$ . Identify the constant of variation and verify it with the graph. Also find $y$ when $x = 9$ .