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

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 Equation . How many more such lines are there, and why?

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

  • Equation and Equation , one possible relation between these is Equation

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

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

    Therefore Equation 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 Equation . Putting the value of the point on the line (2,14) which must satisfy this equation, Equation . Our third equation thus becomes, Equation .

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

    Therefore, Equation 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 Equation lies on the graph of the equation Equation , find the value of a?

Solution:

Give the point Equation lies on the graph of the equation Equation

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

Putting the value Equation and Equation in the given equation we get,

Equation

Equation

Equation

Equation

Equation

Therefore, Equation becomes Equation

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

L.H.S Equation

R.H.S Equation

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

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