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Introduction to Graphs — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSIntroduction to Graphs3 Marks
Question
Observe the toothpick pattern given below: 
$a.$ Imagine that this pattern continues. Complete the table to show the number of toothpicks in the first six terms.
Pattern
$1$
$2$
$3$
$4$
$5$
$6$
Toothpicks
$4$
 
 
$15$
 
  
$b.$ Make a graph by taking the pattern numbers on the horizontal axis and the number of toothpicks on the vertical axis. Make the horizontal axis from $0$ to $10$ and the vertical axis from $0$ to $30.$
$c.$ Use your graph to predict the number of toothpicks in patterns $7$ and $8$. Check your answers by actually drawing them.
$d.$ Would it make sense to join the points on this graph? Explain.
✓

Answer

$a.$ On the basis of given patterns, we can arrange the following table which show the number of toothpicks in the first six terms.
Pattern
 $1$ $2$ $3$ $4$ $5$ $6$
Toothpicks
 $4$ $7$ $10$ $15$ $16$ $19$
Pattern and toothpicks shows the following relation as
$1 \rightarrow 4, 2 \rightarrow 4 + 3 = 7$
$3 \rightarrow 7 + 3 = 10, 4 \rightarrow 10 + 3 = 13$
$5 \rightarrow 13 + 3 = 16, 6 \rightarrow 16, 3 + 19$
$b.$On the basis of given condition, we can draw the following graph

$c.$ the graph follows the $y = 3x + 1$ pattern. If $x = 7$, then $y = 3 × 7 + 1 = 21 + 1 = 22$ and if $x = 8$, then $y = 3 × 8 + 1 = 24 + 1 = 25$
$x$ $7$ $8$
$y$ $22$ $25$
$d.$ Yes, it shows the relation between $x$ and $y$ follows the given pattern $y = 3x + 1$

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