Question

How do you find the slope of $2x-5y=0$?

Answer 1

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.