From the choices given below,choose the correct equation whose graph is shown in the following figure.

  • A
    $x+y=4$
  • B
    $x+y=5$
  • C
    $x+y=6$
  • D
    $3x+2y=12$

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The force exerted to pull a cart is directly proportional to the acceleration produced in the body. Express the statement as a linear equation of two variables and draw the graph of the same by taking the constant mass equal to $6 \,kg$. Read from the graph,the force required when the acceleration produced is $(i)$ $5 \,m/s^2$,$(ii)$ $6 \,m/s^2$.

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Find the points where the graph of the equation $3x + 4y = 12$ cuts the $x$-axis and the $y$-axis.

Write whether the following statement is True or False. Justify your answer:
The graph of the linear equation $x + 2y = 7$ passes through the point $(0, 7).$

If the graph of the equation $ax + 3y = 21$ passes through the point $(5, 2)$,then the value of $a = \ldots$

Write whether the following statements are True or False? Justify your answers.
$(i)$ $ax + by + c = 0$,where $a, b$ and $c$ are real numbers,is a linear equation in two variables.
$(ii)$ $A$ linear equation $2x + 3y = 5$ has a unique solution.
$(iii)$ All the points $(2, 0), (-3, 0), (4, 2)$ and $(0, 5)$ lie on the $x$-axis.

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