NCERT Class 9 Solutions: Linear Equation in Two Variable (Chapter 4) Exercise 4.3 – Part 2

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Give line passing equation y-y1=m(x-x1)

Give Line Passing Equation

Give line passing equation y-y1=m(x-x1)

The slope intercept form for the equation of a line

Equation of the Line Y=Mx + C

The slope intercept form for the equation of a line

Q-2 Give the equation of two lines passing through . How many more such lines are there, and why?

Solution: For lines passing through ; (2, 14) must be a solution. As we will see below there can be infinitely many lines passing through a point , with different coefficients of x and y.

  • and , one possible relation between these is

    Therefore, is one linear equation passing through point (2, 14) with coefficients of x and y being 1 and 1.

  • Second possible equation can be (coefficients of x and y are 1 and -1)

    Therefore is another linear equation passing through point (2, 14).

  • Now we can start adding various coefficients to x and y. Let’s construct an equation of form . Putting the value of the point on the line (2,14) which must satisfy this equation, . Our third equation thus becomes, .

  • Similarly, is satisfied at (2,14) if

    Therefore, is another line passing through (2, 14)

    Like we said there can be infinite equations with different coefficients of x and y. It makes sense because through one point infinite lines can pass.

    Infinite lines can pass through a point

    Infinite Line Through a Point

    Infinite lines can pass through a point

Q-3 If the point lies on the graph of the equation , find the value of a?

Solution:

Give the point lies on the graph of the equation

Since point lies on the equation, it must satisfy this equation.

Putting the value and in the given equation we get,

Therefore, becomes

Check: To check our solutions, we would again substitute, and

L.H.S

R.H.S

So, L.H.S R.H.S and hence our solution was correct.