Slope intercept form: y = mx + c
Re-arrange the equation to get y value on left hand side and everything else on the right:
3y = 4x + 15
Slope intercept form is y = mx + c , so in order to get one y, divide every term by 3
y = 4/3x + 5
Y intercept will happen when x = 0
Therefore, subbing in x = 0;
y = 4/3*0 + 5
y = 5
If by slope you mean the gradient of the line, then the gradient is just the "m" value from y = mx + c
Therefore the gradient would be 4/3.