Question

Find Slope, X- Intercept and Y- Intercept on the line $\dfrac{{3x}}{2} + \dfrac{{2y}}{3} = 0$

Answer 1

Hint: Here, we will convert the given equation of the line in the form of Slope – Intercept form. Then by using the general equation of slope- intercept form of the line, we will find the slope, the $y$- intercept of the given line. Then using any value of $y$ we will find the $x$- intercept

Formula Used:
The Slope- Intercept form is given by the formula $y = mx + c$ where $m$ is the slope and $c$ is the $y$-intercept.

Complete step-by-step answer:
The given equation is $\dfrac{{3x}}{2} + \dfrac{{2y}}{3} = 0$
Now, we will convert the given equation into a slope - intercept form.
Therefore, by taking LCM of the fractions, we get
$ \Rightarrow \dfrac{{3x}}{2} \times \dfrac{3}{3} + \dfrac{{2y}}{3} \times \dfrac{2}{2} = 0$
$ \Rightarrow \dfrac{{9x}}{6} + \dfrac{{4y}}{6} = 0$
Adding the terms, we get
$ \Rightarrow \dfrac{{9x + 4y}}{6} = 0$
Multiplying 6 on both sides, we get
$ \Rightarrow 9x + 4y = 0$
Subtracting $9x$ on both the sides, we get
$ \Rightarrow 4y = - 9x$
Dividing both sides by 4, we get
$ \Rightarrow y = - \dfrac{9}{4}x$
Thus the equation $y = - \dfrac{9}{4}x$ is of the Slope- Intercept form $y = mx + c$
Comparing the equation with $y = mx + c$, we get
$m = - \dfrac{9}{4}$ and $c = 0$
Thus, the slope of the line $\dfrac{{3x}}{2} + \dfrac{{2y}}{3} = 0$ is $ - \dfrac{9}{4}$ , the $y$-intercept of the line $\dfrac{{3x}}{2} + \dfrac{{2y}}{3} = 0$is $0$.
Now, we will find the $x$ – intercept.
Now, substituting $y = 0$ in the equation $y = - \dfrac{9}{4}x$, we get
$ \Rightarrow 0 = - \dfrac{9}{4}x$
Now, by rewriting the equation, we get
$ \Rightarrow x = 0$
Thus, the $x$ – intercept of the line $\dfrac{{3x}}{2} + \dfrac{{2y}}{3} = 0$is $0$.
Therefore, the slope of the line $\dfrac{{3x}}{2} + \dfrac{{2y}}{3} = 0$ is $ - \dfrac{9}{4}$ , the $y$-intercept of the line $\dfrac{{3x}}{2} + \dfrac{{2y}}{3} = 0$is $0$or $\left( {0,0} \right)$ and the \[x\] – intercept of the line $\dfrac{{3x}}{2} + \dfrac{{2y}}{3} = 0$is $0$or $\left( {0,0} \right)$ .

Note: We know that the equation of line can be expressed in the form of slope-intercept form, intercept form and normal form. A slope is defined as the ratio of change in the $y$ axis to the change in the \[x\] axis. Slope can be represented in the parametric form and in the point form. A point crossing the \[x\]-axis, it is called \[x\]-intercept and the point crossing the $y$-axis is called the $y$-intercept.