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How do you find slope and intercept of the given linear equation, the equation is \[5x + 2y = 10\]?

Last updated date: 23rd Jul 2024
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Hint: Slope is the angle from the positive axis of the graph to the line drawn; it gives the angle of inclination of the graph. To find the slope of any line you can use trigonometric identity of “tanx” where “x” is the ratio of perpendicular length and base length, now to find the intercept which means the points on which the curve is cutting the axis of graph can be found out by some simplification in the equation.

Complete step by step solution:
The given equation is \[5x + 2y = 10\]
According to the question we have to find the slope and intercept of the curve given, lets first find the slope of the graph.
For finding slope we are using here the differentiation method of finding slope, in which we have to differentiate the equation as \[\dfrac{{dy}}{{dx}}\]
Now finding the value of “y” from the equation by rearranging the term we get:
\Rightarrow 5x + 2y = 10 \\
\Rightarrow 2y = 10 - 5x \\
\Rightarrow y = \dfrac{{10 - 5x}}{2} \\
\Rightarrow y = 5 - \dfrac{5}{2}x \\
Now on differentiating the term we get:
\Rightarrow \dfrac{{dy}}{{dx}} = \dfrac{d}{{dx}}\left( {5 - \dfrac{5}{2}x} \right) \\
\Rightarrow \dfrac{{dy}}{{dx}} = 0 - \dfrac{{ -
5}}{2}( \text{differentiation of ‘x’ with respect to ‘x’ is 1 and differentiation of constant term is zero} ) \\
Hence we find the required slope of the given equation.
Now for finding the intercept we have to rearrange the equation as, the general equation which is:
\[ \Rightarrow \dfrac{x}{a} + \dfrac{y}{b} = 1\,(\text{here ‘a’ and ‘b’ are intercepts of the given equation})\]
Rearranging our equation we get:
\Rightarrow \dfrac{{5x}}{{10}} + \dfrac{{2y}}{{10}} =
1(\text{dividing by 10 both the sides of the equation}) \\
\Rightarrow \dfrac{x}{2} + \dfrac{y}{5} = 1 \\
\Rightarrow \text{intercepts are }\dfrac{1}{2},\dfrac{1}{5}\,for\,x\,and\,y\,respectively
This is our final answer.

Note: Here it was easy to rearrange the equation in the general form of the intercept equation but if this rearrangement is not possible then you have to plot the graph and then check the points on which the curve is cutting both axes and that coordinates are our required intercepts.