Express $y$ in terms of $x$ from the linear equation $3x - 2y + 6 = 0$. Also, find the coordinates of the point where this line cuts the y-axis.

Q: Express $y$ in terms of $x$ from the linear equation $3x - 2y + 6 = 0$. Also, find the coordinates of the point where this line cuts the y-axis.

Given linear equation is: $$3x - 2y + 6 = 0$$ \nRearranging to express $y$ in terms of $x$: $$2y = 3x + 6$$ $$y = \frac{3x + 6}{2}$$ \nTo find the point where the line intersects the y-axis, set $x = 0$ in the above relation: $$y = \frac{3(0) + 6}{2} = \frac{6}{2} = 3$$ \nTherefore, $y$ expressed in terms of $x$ is $y = \frac{3x + 6}{2}$, and the coordinates of the point where the line cuts the y-axis are $(0, 3)$.

Question

Accepted Answer

Given linear equation is: $$3x - 2y + 6 = 0$$ 
Rearranging to express $y$ in terms of $x$: $$2y = 3x + 6$$ $$y = \frac{3x + 6}{2}$$ 
To find the point where the line intersects the y-axis, set $x = 0$ in the above relation: $$y = \frac{3(0) + 6}{2} = \frac{6}{2} = 3$$ 
Therefore, $y$ expressed in terms of $x$ is $y = \frac{3x + 6}{2}$, and the coordinates of the point where the line cuts the y-axis are $(0, 3)$.

MP Board · Class 10 · Mathematics · Pair of Linear Equations in Two VariablesExpress $y$ in terms of $x$ from the linear equation $3x - 2y + 6 = 0$. Also, find the coordinates of the point where this line cuts the y-axis.