Question

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

Answer 1

In this question, we have to make a given equation in the form of slope intercept form of a line. It can be done by first subtracting $2x$ from both sides of the equation. Then, divide each term in the equation by $- 5$. Then compare the final equation with the standard slope intercept form of a line and find the slope $m$ and an intercept $c$ on $y$-axis for this equation.

Complete step by step answer:
We know that the slope intercept form of a line is the equation of a line with slope $m$ and making an intercept $c$ on $y$-axis is $y = mx + c$.
Given equation is $2x - 5y = 0$
So, we have to make a given equation in the form of $y = mx + c$, the equation of a line with slope $m$ and making an intercept $c$ on $y$-axis.
First, subtract $2x$ from both sides of the above equation.
$\Rightarrow - 5y = - 2x$
Now, divide each term in the equation by $- 5$.
$\Rightarrow \dfrac{{ - 5y}}{{ - 5}} = \dfrac{{ - 2x}}{{ - 5}}$
It can be written as
$\Rightarrow y = \dfrac{2}{5}x$
Now, compare this equation with the standard slope intercept form of a line and find the slope $m$ and an intercept $c$ on $y$-axis for this equation.
Here, $m = \dfrac{2}{5}$ and $c = 0$.

Therefore, the slope of given line is $\dfrac{2}{5}$ and $y$-intercept is $0$.

Note: For a line making acute angle with the $x$-axis, the slope is positive as the behaviour of $y$ is same as that of $x$, i.e., the value of $y$ increases as the value of $x$ increases and the value of $y$ decreases when the value of $x$ decreases. We can also find the $y$ intercept of the line by putting $x = 0$ in the equation as when the line is cutting the $y$-axis the value of $x$ is 0.