Question

How do you find the slope of \[2x-5y=0\]?

Answer 1

Hint: Write the given equation in slope – intercept form. To do this, keep the variable y in the L.H.S. and take all other terms to the R.H.S. Now, make the coefficient of y equal to 1 and compare the obtained equation with \[y=mx+c\]. Here, ‘m’ will be the slope of the line and ‘c’ will be its intercept.

Complete step by step answer:
Here, we have been provided with the linear equation \[2x-5y=0\] and we have been asked to find the slope of this line. But first we need to know about the slope – intercept form of a linear equation.
Now, we know that we can write a linear equation of a straight line in many forms like: - standard form, slope – intercept form, poplar form, parametric form etc. But here we need to see the slope – intercept form.
In slope – intercept form we write the equation of a line as \[y=mx+c\], where ‘m’ represents the slope and ‘c’ represents the intercept on y – axis. Here, we have been provided with the equation: - \[2x-5y=0\]. So, keeping the term containing the variable ‘y’ in the L.H.S. and taking all other terms to the R.H.S., we get,
\[\Rightarrow -5y=-2x\]
Dividing both the sides with -5 we get,
\[\Rightarrow y=\left( \dfrac{2}{5} \right)x\] - (1)
Now, when we compare equation (1) with the relation \[y=mx+c\], we can conclude that we have,
\[\Rightarrow \] Slope of the given line = \[m=\dfrac{2}{5}\].

Hence, \[\dfrac{2}{5}\] is the slope and our answer.

Note: One may note that you can remember the formula of the slope of a straight line whose equation is in standard form given as: - \[ax+by+c'=0\]. Here, slope is given as \[\dfrac{-b}{a}\]. You can also determine the y – intercept for this form given as: - \[\dfrac{-c'}{a}\]. In the above question as you can see that the constant term (c) is 0, that means the y – intercept is 0. You must remember all the forms of a straight line, like: - slope – intercept form, point – slope form, polar form, standard form etc.