Write each of the following equations in the form $ax + by + c = 0$ and indicate the values of $a$, $b$ and $c$ in each case :
$(i)$ $2 x+3 y=4.37$
$(ii)$ $x-4=\sqrt{3} y$
$(iii)$ $4=5 x-3 y$
$(iv)$ $2 x=y$
Write each of the following equations in the form $ax + by + c = 0$ and indicate the values of $a$, $b$ and $c$ in each case :
$(i)$ $2 x+3 y=4.37$
$(ii)$ $x-4=\sqrt{3} y$
$(iii)$ $4=5 x-3 y$
$(iv)$ $2 x=y$
$(i)$ $2x + 3y = 4.37$ can be written as $2x + 3y -4.37 = 0$.
Here $a = 2$, $b = 3$ and $c = -\, 4.37$.
$(ii)$ The equation $x-4=\sqrt{3} y$ can be written as $x-\sqrt{3} y-4=0 .$
Here $a=1$, $b=-\,\sqrt{3}$ and $c=-\,4$
$(iii)$ The equation $4=5 x-3 y$ can be written as $5 x-3 y-4=0 .$
Here $a=5, b=-3$ and $c=-\,4 .$
$(iv)$ The equation $2x = y$ can be written as $2x -y + 0 = 0$.
Here $a = 2, \,b = -\,1$ and $c = 0.$
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In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius :
$F =\left(\frac{9}{5}\right) C +32$
$(i)$ Draw the graph of the linear equation above using Celsius for $x$ - axis and Fahrenheit for $y$ - axis.
$(ii)$ If the temperature is $30\,^oC$, what is the temperature in Fahrenheit ?
$(iii)$ If the temperature is $95\,^oF$, what is the temperature in Celsius ?
$(iv)$ If the temperature is $0\,^oC$ , what is the temperature in Fahrenheit and if the temperature is $0\,^oF$ , what is the temperature in Celsius ?
$(v)$ Is there a temperature which is numerically the same in both Fahrenheit and Celsius ? If yes, find it.
In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius :
$F =\left(\frac{9}{5}\right) C +32$
$(i)$ Draw the graph of the linear equation above using Celsius for $x$ - axis and Fahrenheit for $y$ - axis.
$(ii)$ If the temperature is $30\,^oC$, what is the temperature in Fahrenheit ?
$(iii)$ If the temperature is $95\,^oF$, what is the temperature in Celsius ?
$(iv)$ If the temperature is $0\,^oC$ , what is the temperature in Fahrenheit and if the temperature is $0\,^oF$ , what is the temperature in Celsius ?
$(v)$ Is there a temperature which is numerically the same in both Fahrenheit and Celsius ? If yes, find it.
Write each of the following as an equation in two variables :
$(i)$ $x=-\,5$
$(ii)$ $y=2$
$(iii)$ $2x=3$
$(iv)$ $5y=2$
Write each of the following as an equation in two variables :
$(i)$ $x=-\,5$
$(ii)$ $y=2$
$(iii)$ $2x=3$
$(iv)$ $5y=2$
Given the point $(1,\, 2)$, find the equation of a line on which it lies. How many such equations are there ?
Given the point $(1,\, 2)$, find the equation of a line on which it lies. How many such equations are there ?
From the choices given below, choose the equation whose graphs are given in Fig. $(i)$ and Fig. $(ii)$.
For Fig. $(i)$ For Fig. $(ii)$
$(a)$ $y=x$ $(a)$ $y=x+2$
$(b)$ $x+y=0$ $(b)$ $y=x-2$
$(c)$ $y=2 x$ $(c)$ $y=-x+2$
$(d)$ $2+3 y=7 x$ $(d)$ $x+2 y=6$
From the choices given below, choose the equation whose graphs are given in Fig. $(i)$ and Fig. $(ii)$.
For Fig. $(i)$ For Fig. $(ii)$
$(a)$ $y=x$ $(a)$ $y=x+2$
$(b)$ $x+y=0$ $(b)$ $y=x-2$
$(c)$ $y=2 x$ $(c)$ $y=-x+2$
$(d)$ $2+3 y=7 x$ $(d)$ $x+2 y=6$