There are several ways to approach this problem. One simple way is to observe that when x increases by 1, f(x) always increases by 2. Since f(x) always increases by 2 when x increases by 1, it can be written in the form y = mx + c and is hence a linear function.

The slope will be the value that f(x) increases by when x increases by 1. As observed above, this is 2. Hence, the slope is 2.

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Let us look at what happens when the x value increases. As x goes from 1 to 2, the y value increases by 6. As x goes from 2 to 3, the y value increases by 3. We do not need to go further. Since the value of y increases by different values when increase the x value by 1, the function is definitely not linear.

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For the linear function f(x)=3x+6, (a) Determine the slope and y-intercept (b) Use the slope and y-intercept to graph the linear function. (c) Determine the average rate of change of the function. (d) Determine whether the linear function is increasing, decreasing, or constant.

The slop is___? Could you write down how you got the answer step by step, thanks.

The way you should graph is that the first thing you should do is to mark the x and y intercepts and the vertex. If possible, draw a dotted line through the axis of symmetry and then draw an inverted parabola through those 3 points. It should look like this: