Question

Make a table for the values of a and y for the equations, and use it to graph the relationship. (a) y = 4x (b) y = -2x​

Answer 1

Answer:

For fig. (i) For fig. (ii)

(i) y=x (i) y=x+2

(ii) x+y=0 (ii) y=x−2

(iii) y=2x (iii) y=−x+2

(iv) 2+3y=7x (iv) x+2y=6

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Medium

Solution

verified

In the given fig. (i), the solutions of the equation are (−1,1),(0,0) and (1,−1).

∴ the equation which satisfies these solutions is the correct equation.

Equation (ii) x+y=0, satisfies these solutions.

Proof:

If we put the value of x=−1 and y=1 in the equation x+y=0

=x+y=−1+1=0

∴L.H.S=R.H.S

if we put the the value of x = 0 and y = 0

=x+y=0+0=0

∴L.H.S=R.H.S

If we put the value of x=1 and y=−1

=x+y=1+(−1)=1–1=0

L.H.S=R.H.S

Hence, option (ii) x+y=0 is correct.

In the given Fig.(ii) the solutions of the equation are (−1,3),(0,2) and (2,0).

∴The equation which satisfies these solutions is the correct equation.

Equation (iii) y=−x+2 , satisfies these solutions.

Proof:

If we put the value of x=−1 and y=3 in the equation y=−x+2

y=−x+2

3=−(−1)+2

3=3

∴L.H.S=R.H.S

if we put the the value of x=0 and y=2

y=−x+2

2=−0+2

2=2

∴L.H.S=R.H.S

If we put the value of x=2 and y=0

y=−x+2

0=−2+2

0=0

L.H.S=R.H.S

Hence, option (iii) y=−x+2 is correct.