check the picture below.
a positive slope, means an increasing slope, namely, a line that is higher from left-to-right, so the right tip of it is going upwards. A negative y-intercept,
now, if you notice the 3 green lines, the line is increasing, the right-side is higher than the left-side, and the y-intercept, namely where x = 0, or where the graph touches the y-axis, their y-intercept is on a negative value of y.
now, look at the red line, it has also a positive slope, is increasing, however, there's no way it can have negative y-intercept. If it remains increasing, it can only have a y-intercept of 3 or higher, but not lower than that. The only way it can have a negative value for the y-intercept is if it tips over, but if we do that, the slope will be decreasing.