Consider the acceleration graph. if the mass of the object that is accelerating does not change, but the force applied is tripled, how would the slope of the line change?

The graph is missing but I guess you refer to the "Force vs mass" graph. In this graph, the acceleration is the slope of the curve, because the relationship between force F, mass m and acceleration a is (Second Newton's law)
F= ma
And in the graph, m is the x-variable, F is the y-variable and a the slope.

We can notice that there is a direct proportionality between F and a. So, if m is constant, when we triple the force (F' = 3F), the acceleration will also triple (a'=3 a). But since the acceleration is the slope of the curve, this means that the new slope will be 3 times the slope of the original curve.

Alinear relationship would look like a straight line on the graph. it could have a positive negative or 0 slope. so it could be a line potentially going in any direction but it must be perfectly straight.