The line through $\mathrm{P}(5,3)$ intersects $y$-axis at $\mathrm{Q}$.

   

Write the equation of the line.

The line through $\mathrm{P}(5,3)$ intersects $y$-axis at $\mathrm{Q}$.

Find the co-ordinates of $\mathrm{Q}$.

Write down the equation of the line whose gradient is $-\frac{2}{5}$ and which passes through point $\mathrm{P}$, where $\mathrm{P}$ divides the line segment joining $\mathrm{A}(4,-8)$ and $\mathrm{B}(12,0)$ in the ratio $3: 1$.

Find the slope and $y$-intercept of the line $y=4$.

Find the slope and $y$-intercept of the line $ax-by=0$.

Find the slope and $y$-intercept of the line $3x-4y=5$.