Linear Equation Slope

For the system to have no solutions, the determinant of the matrix should be zero. So, 4*10 = 3*k. So, k = 13.33

The y intercept of a line y = mx+c is c
Rewriting the equation of the line in this form, 9y/32 = x- k
y = 32x/9 - 32k/9
The y intercept = -32k/9
Since k is a negative number, - k is positive. For large y intercept, |k| should be large.

If both the equations are the same then the lines are coincident and there are infinite solutions. That is possible when p = 7/4, which is obtained by rearranging the first equation.