Question

what is the slope of the line represented by 5x-12y=24?

Answer 1

We have to find out slope of the line represented by 5x-12y=24.

To find the slope of line we will transform given equation of line in the form of :- y = mx+c. Where m is slope of line.

$\rm \longrightarrow \: 5x-12y=24 \\ \\ \\ \rm \longrightarrow \: -12y=24 - 5x\\ \\ \\ \rm \longrightarrow \: 12y=5x - 24\\ \\ \\ \rm \longrightarrow \: y=(5x - 24) \frac{1}{12} \\ \\ \\ \rm \longrightarrow \: y= \dfrac{5x}{12} - \dfrac{24}{12} \\ \\ \\ \rm \longrightarrow \: y= \dfrac{5x}{12} -2$

Therefore, slope of line = (5/12)

Additional Information :

$\rm \: Equation \: of \: line \: passing \: through \: points \: (x_1 , y_1) \: and \: (x_2 , y_2) :$

$\tt \longrightarrow y - y_1 = x-x_1\bigg( \dfrac{y_2-y_1}{ x_2-x_1} \bigg )$

$\rm \rightarrow \: here \: \bigg( \dfrac{y_2-y_1}{ x_2-x_1} \bigg ) is \: slope \: of \: line.$

Answer 2

$\huge {AηsωeR} ✍$

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✏️There are three methods to find the slope of given line :-

✏️Method :- 1

Reduce the given line to slope intercept form (y = mx + c) and then on comparing we get the value of m, which is slope of line.

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✏️Method :- 2

If the equation of the line is ax + by + c = 0, then slope is

$\bf \:m = - \dfrac{coefficient \: of \: x}{coefficient \: of \: y}$

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Method :- 3

Differentiate the equation of line w. r. t. x and then slope is

$\bf \:m \: = \dfrac{dy}{dx}$

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✏️Rationale :-

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${{ \boxed{{\bold\blue{✏By \: Method :- 1 }}}}}$

The equation of line is 5x - 12y = 24

$\sf \:  ⟼ - 12y = - 5x + 24$

☆ Divide both sides by - 12, we get

$\sf \:  ⟼y = \dfrac{5}{12} x - 2$

☆On comparing with y = mx + c, we get

$\bf\implies \:m = \dfrac{5}{12}$

${{ \boxed{\large{\bold\blue{Hence, \: slope \: of \: line \: is \: \dfrac{5}{12} }}}}}$

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${{ \boxed{{\bold\blue{✏By \: Method :- 2 }}}}}$

The equation of line is 5x - 12y = 24

We know,

$\bf \:m = - \dfrac{coefficient \: of \: x}{coefficient \: of \: y}$

$\sf\implies \:m \: = - \dfrac{5}{ - 12} = \dfrac{5}{12}$

${{ \boxed{\large{\bold\blue{Hence, \: slope \: of \: line \: is \: \dfrac{5}{12} }}}}}$

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${{ \boxed{{\bold\blue{✏By \: Method :- 3 }}}}}$

The equation of line is 5x - 12y = 24

☆Differentiate w. r. t. x, we get

$\sf \:  \dfrac{d}{dx} (5x - 12y) = \dfrac{d}{dx} 24$

$\sf\implies \:5 - 12\dfrac{dy}{dx} = 0$

$\sf\implies \: - 12\dfrac{dy}{dx} = - 5$

$\sf\implies \:\dfrac{dy}{dx} = \dfrac{5}{12}$

${{ \boxed{\large{\bold\blue{Hence, \: slope \: of \: line \: is \: \dfrac{5}{12} }}}}}$

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