Find the equation of a line which has Y intercept $4$ and is parallel to the line $2x - 3y = 7$. Find the coordinates of the point where it cuts the X-axis.
Y intercept $= c = 4$
Given line: $2x - 3y = 7$
i.e. $\;$ $y = \dfrac{2}{3}x - \dfrac{7}{3}$
Slope of the given line $= m = \dfrac{2}{3}$
Since the required line is parallel to the given line, slope of required line $= m = \dfrac{2}{3}$
Let the equation of the required line be $\;$ $y = mx + c$
i.e. $\;$ $y = \dfrac{2}{3} x + 4$
i.e. $\;$ $2x - 3y = -12$
When the line cuts the X-axis, its Y coordinate is $0$.
Then we have, $\;$ $2x = -12$ $\implies$ $x = -6$
The required line cuts the X-axis at the point $\left(-6,0\right)$.