Question

Question :
In a city, the taxi fare for the 1st kilometre is ₹10 and the fare for subsequent distance is ₹6 per km. Taking the distance covered as "x" km and total fare as Rs "y", write a linear equation for this information and draw it's graph.

All the best!​

Answer 1

Answer of the above mentioned.

Answer 2

AnswEr :

Let's consider that , The Total Distance covered by Taxi as X km and Total fare as Rs. Y .

⠀⠀⠀⠀(I) Fare for , the First kilo metre Taxi charges ₹10 &

$\\\::\implies \sf \: Fare\:_{\:(1^{st} \:\: km)}\:=\: Rs.\:10\:$

⠀⠀⠀⠀(II) The fare for subsequent distance is ₹6 per km.

$\\\::\implies \sf \: Fare\:_{\:( Rest \:\:Distance)}\:=\: Rs.\:6\:\times \:Remaining \:Distance \:$

$\::\implies \sf \: Fare\:_{\:( Rest \:\:Distance)}\:=\: Rs.\:6\:(\: Total \:Distance \:-\:1\:)\:$

$\::\implies \sf \: Fare\:_{\:( Rest \:\:Distance)}\:=\: Rs.\:6\:(\: X \:-\:1\:)\:$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

☯ Total Fare charges by the Taxi will be –

⠀⠀⠀⠀

$\longrightarrow \sf\:Total \:Fare\:=\:Fare\:_{\:(1^{st} \:\: km)}\:\:+\:Fare\:_{\:( Rest \:\:Distance)}\:$

$\longrightarrow\sf \:Y\:=\:10\:+\:6\:(\: X \:-\:1\:)\: \:$

$\longrightarrow\sf \:Y\:=\:10\:+\:(\: 6X \:-\:6\:)\: \:$

$\longrightarrow \sf\:Y\:=\:10\:+\: 6X \:-\:6 \:$

$\longrightarrow \sf\:Y\:=\:\: 6X + 4 \:$

$\longrightarrow\sf \:Y\:=\:\: 6X + 4 \:\qquad \bigg\lgroup Linear \: Equation \:\bigg\rgroup$

$\longrightarrow \sf\pmb{\sf\:Y\:=\:\: 6X + 4 \:}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

☯ Graph For the Linear Equation –

⠀⠀⠀⠀

⠀⠀⠀⠀▪︎ To Draw the graph , we need at least two solutions of the Equation .

$\\\\\qquad \dag\:\underline {\sf Substituting \: \:\pmb{\sf X \:=\:0\: }\: in \: Equation \::\:}$

$\dashrightarrow\sf \:Y\:=\:\: 6X + 4 \:$

$\dashrightarrow\sf \:Y\:=\:\: 6(0) + 4 \:$

$\dashrightarrow\sf \:Y\:=\:\: 0 + 4 \:$

$\dashrightarrow \sf\:Y\:=\:\: 4 \:$

⠀⠀⠀⠀ So , ( 0 , 4 ) is the one Solution of Equation .

$\\\qquad \dag\:\underline {\sf Substituting \: \:\pmb{\sf X \:=\:1\: }\: in \: Equation \::\:}$

$\dashrightarrow\sf \:Y\:=\:\: 6X + 4 \:$

$\dashrightarrow\sf \:Y\:=\:\: 6(1) + 4 \:$

$\dashrightarrow\sf \:Y\:=\:\: 6 + 4 \:$

$\dashrightarrow \sf\:Y\:=\:\: 10 \:$

⠀⠀⠀⠀ So , ( 1 , 10 ) is the second Solution of Equation .

⠀⠀⠀⠀

⠀》 Now , By Plotting these Points [ ( 0 , 4 ) & ( 1 , 10 ) ] on the Graph we get –

Kindly view attachment for the Graph .