Medium
Draw the graphs of linear equations $y=x$ and $y=-x$ on the same Cartesian plane.
What do you observe?
What do you observe?
(N/A) Any point on the graph of $y = x$ will have $x$ and $y$ coordinates that are identical. The line passes through the points $(0,0), (1,1),$ and $(-1,-1).$
Similarly,any point on the graph of $y = -x$ will have $x$ and $y$ coordinates of opposite signs. The line passes through the points $(1,-1)$ and $(-1,1).$
Also,the point $(0,0)$ satisfies the equation $y = -x.$
The graphs of the linear equations $y = x$ and $y = -x$ on the same Cartesian plane are shown in the figure below.
We observe that the graphs of both these equations intersect at the origin $(0,0).$
Similarly,any point on the graph of $y = -x$ will have $x$ and $y$ coordinates of opposite signs. The line passes through the points $(1,-1)$ and $(-1,1).$
Also,the point $(0,0)$ satisfies the equation $y = -x.$
The graphs of the linear equations $y = x$ and $y = -x$ on the same Cartesian plane are shown in the figure below.
We observe that the graphs of both these equations intersect at the origin $(0,0).$
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If the temperature of a liquid can be measured in Kelvin units as $x^{\circ} K$ or in Fahrenheit units as $y^{\circ} F$,the relation between the two systems of measurement of temperature is given by the linear equation
$y = \frac{9}{5}(x - 273) + 32$
$(i)$ Find the temperature of the liquid in Fahrenheit if the temperature of the liquid is $313^{\circ} K$.
$(ii)$ If the temperature is $158^{\circ} F$,then find the temperature in Kelvin.
$y = \frac{9}{5}(x - 273) + 32$
$(i)$ Find the temperature of the liquid in Fahrenheit if the temperature of the liquid is $313^{\circ} K$.
$(ii)$ If the temperature is $158^{\circ} F$,then find the temperature in Kelvin.
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View SolutionWrite 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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$(ii)$ $A$ 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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View SolutionWrite whether the following statements are True or False? Justify your answers.
$(i)$ The line parallel to the $y$-axis at a distance of $4$ units to the left of the $y$-axis is given by the equation $x = -4$.
$(ii)$ The graph of the equation $y = mx + c$ passes through the origin.
$(i)$ The line parallel to the $y$-axis at a distance of $4$ units to the left of the $y$-axis is given by the equation $x = -4$.
$(ii)$ The graph of the equation $y = mx + c$ passes through the origin.
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View SolutionThe following values of $x$ and $y$ are thought to satisfy a linear equation:
$x$ $1$ $2$ $y$ $1$ $3$
Draw the graph,using the values of $x, y$ as given in the above table.
At what point does the graph of the linear equation:
$(i)$ cut the $x$-axis?
$(ii)$ cut the $y$-axis?
| $x$ | $1$ | $2$ |
| $y$ | $1$ | $3$ |
Draw the graph,using the values of $x, y$ as given in the above table.
At what point does the graph of the linear equation:
$(i)$ cut the $x$-axis?
$(ii)$ cut the $y$-axis?
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