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Reduce the following equations into slope – intercept form and find their slopes and the y – intercepts. (i) x + 7y = 0 (ii) 6x + 3y – 5 = 0
Reduce the following equations into slope – intercept form and find their slopes and the y – intercepts. (i) x + 7y = 0 (ii) 6x + 3y – 5 = 0
Class 11 | Exercise 10.3 | Maths | NCERT | Straight Lines
Reduce the following equations into slope – intercept form and find their slopes and the y – intercepts. (i) x + 7y = 0 (ii) 6x + 3y – 5 = 0

As indicated by the inquiry,

 

\[~\left( \mathbf{i} \right)\text{ }\mathbf{x}\text{ }+\text{ }\mathbf{7y}\text{ }=\text{ }\mathbf{0}\]

Given:

 

The condition is \[\mathbf{x}\text{ }+\text{ }\mathbf{7y}\text{ }=\text{ }\mathbf{0}\]

Slant – catch structure is addressed in the structure\[\mathbf{y}’\text{ }=\text{ }\mathbf{mx}\text{ }+\text{ }\mathbf{c}’\] , where m is the slant and c is the y capture

 

In this way, the above condition can be communicated as

 

\[\mathbf{y}\text{ }=\text{ }-\text{ }\mathbf{1}/\mathbf{7x}\text{ }+\text{ }\mathbf{0}\]

∴ The above condition is of the structure\[\mathbf{y}\text{ }=\text{ }\mathbf{mx}\text{ }+\text{ }\mathbf{c}\] , where \[\mathbf{m}\text{ }=\text{ }-\text{ }\mathbf{1}/\mathbf{7}\] and \[\mathbf{c}\text{ }=\text{ }\mathbf{0}.\]

\[\left( \mathbf{ii} \right)\text{ }\mathbf{6x}\text{ }+\text{ }\mathbf{3y}\text{ }\text{ }\mathbf{-5}\text{ }=\text{ }\mathbf{0}\]

Given:

 

The condition is \[\mathbf{6x}\text{ }+\text{ }\mathbf{3y}\text{ }\text{ }\mathbf{-5}\text{ }=\text{ }\mathbf{0}\]

 

Slant – catch structure is addressed in the structure\[\mathbf{y}’\text{ }=\text{ }\mathbf{mx}\text{ }+\text{ }\mathbf{c}’\] , where m is the slant and c is the y capture

 

In this way, the above condition can be communicated as

 

\[\mathbf{3y}\text{ }=\text{ }-\text{ }\mathbf{6x}\text{ }+\text{ }\mathbf{-5}\]

\[\mathbf{y}\text{ }=\text{ }-\text{ }\mathbf{6}/\mathbf{3x}\text{ }+\text{ }\mathbf{-5}/\mathbf{3}\]

\[=\text{ }-\text{ }\mathbf{2x}\text{ }+\text{ }\mathbf{5}/\mathbf{3}\]

∴ The above condition is of the structure\[\mathbf{y}\text{ }=\text{ }\mathbf{mx}\text{ }+\text{ }\mathbf{c}\] , where \[\mathbf{m}\text{ }=\text{ }-\text{ }\mathbf{2}\] and \[\mathbf{c}\text{ }=\text{ }\mathbf{5}/\mathbf{3}.\]

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