Question

please answer this question ​

Answer 1

SOLUTION

We draw a graph ( Distance, cost)

If (x, y) is point on the line the

x - coordinate = Abscissa represents Distance and

y - coordinate = Ordinate represents Cost

So the points are (10,15), (20,25), (30,35), (50,55)

On plotting the points on the graph we get the points A (10,15), B(20,25), C(30,35), D(50,55)

From graph it is observed that we get a straight line

Again the equation of the line passing through the points A (10,15), B(20,25) is

$\displaystyle \sf{ \frac{y - 15}{x - 10} = \frac{25 - 15}{20 - 10} }$

$\implies \displaystyle \sf{ \frac{y - 15}{x - 10} = \frac{10}{10} }$

$\implies \displaystyle \sf{ \frac{y - 15}{x - 10} = 1 }$

$\implies \displaystyle \sf{ y - 15 = x - 10}$

$\implies \displaystyle \sf{y = x + 5 }$

(i) If he drives 40 km

Then Abscissa of the point = 40

Accordingly ordinate = 45

The point is G(40,45)

So the cost = ₹ 45

From Equation of the line it can also verified

As he drives 40 km

So x = 40

∴ y = 40 + 5 = 45

(ii) He spends ₹ 44

So the ordinate = 44

Accordingly from graph Abscissa = 39

The point is H (44,39)

So the distance covered = 39 km

From Equation of the line it can also verified

As he spends ₹ 44

So y = 44

∴ x = 44 - 5 = 39

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