Give the equations of two lines passing through (3 16 how many more such lines are there why)

The taxi fare in a city is as follows: For the first kilometre, the fare is Rs 8 and for the subsequent distance it is Rs 5 per km. Taking the distance covered as x km and total fare as Rs y, write a linear equation for this information, and draw its graph.

Total distance covered = x kmTotal fare = Rs yFare for the first kilometre = Rs 8Subsequent distance = (x – 1) kmFare for the subsequent distance = Rs 5(x – 1)According to the question,y = 8 + 5 (x – 1)⇒ y = 8 + 5x – 5⇒ y = 5x + 3

Table of solutions

We plot the points (0, 3) and (1, 8) on the graph paper and join the same by a ruler to get the line which is the graph of the equation y = 5x + 3.

Text Solution

Solution : "Solution<br>Given point is `'(3,12)'`<br>⟹`'x=3,y=12'`<br>The lines formed can be `x+y=3+12=15,x−y=3−12=−9`<br> The two lines passing through `(3,12)` are `x+y=15,x−y=−9`<br> Also `y=4x,5x−y=3`,⋯ lines passes through '`(3,12)`'<br> There are infinitely many lines passing through `'(3,12)'`. Since many lines can be drawn through a given point "

Solution:

Given: Point (2, 14) at which lines passing through.

We can think of framing equations that could satisfy the given point (2, 14) on the line.

It can be observed that point (2, 14) satisfies the equation 7x - y = 0 and x - y + 12 = 0.

Therefore, 7x - y = 0 and x - y + 12 = 0 are two lines passing through point (2, 14).

Since we know infinite lines can pass through a single point, therefore there are infinite more lines passing through the given point

☛ Check: NCERT Solutions Class 9 Maths Chapter 4

Video Solution:

Give the equations of two lines passing through (2, 14). How many more such lines are there, and why?

NCERT Solutions Class 9 Maths Chapter 4 Exercise 4.3 Question 2

Summary:

The equations of two lines passing through (2, 14) are 7x − y = 0 and x − y + 12 = 0, there are infinite lines passing through the given point (2, 14).

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Give the equations of two lines passing through 3, 12 . How many more such lines are there, and why?

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