How would a graph of negative and positive acceleration differ?
This depends on what the graph represents. If it is a graph of velocity on the vertical and time on the horizontal, then if acceleration is at a constant rate, the graph will be a straight line with positive slope (pointing 'up'). If acceleration stops, then the graph will be a horizontal line (zero acceleration or deceleration). If it is deceleration (negative acceleration), then the graph will have negative slope (pointing down).
A motion described as a changing, positive velocity results in a sloped line when plotted as a velocity-time graph. If the acceleration is zero, then the slope is zero (i.e., a horizontal line). If the acceleration is positive, then the slope is positive (i.e., an upward sloping line). If the acceleration is negative, then the slope is negative (i.e., a downward sloping line).
If the acceleration is increasing with time will the velocity graph be a straight line concave up or concave down?
Concave up. "Acceleration is increasing with time" tells us that the derivative of acceleration is positive. Since acceleration is the derivative of velocity, this means that the second derivative of velocity is positive. By definition, having a non-negative second derivative means that velocity is concave up.