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We want to find the rate of change for the linear function in the following diagram.

We can see that the graph passes through the points $(1,4)$ and $(2,6).$ Let's mark these points in the diagram.Let's draw arrows to show what it looks like to move from one point to the other by taking one horizontal step followed by a vertical. The horizontal step we label $Δx$ and the vertical $Δy.$

In the diagram we can see that $Δx=1$ and $Δy=2.$ By using these values in the relationship $rate of change=ΔxΔy $ we find the rate of change. Thus, the rate of change for the graphed function is $2.$ b

Observing the given graph, we can see that the line passes through the points $(0,6)$ and $(1.5,0).$ We can move from one point to the other by taking one horizontal step, $Δx,$ followed by a vertical step, $Δy.$

We can in the graph see that the horizontal step we take is $1.5,$ making $Δx=1.5.$ The vertical step is down $6$ units. Moving down makes the step negative. Therefore, $Δy=-6.$ We find the rate of change using this relationship. $rate of change=ΔxΔy $ Let's use the values we have found to calculate the rate of change. We have found that the rate of change for the linear function is $-4.$