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# Writing Linear Functions

## Writing Linear Functions 1.2 - Solution

a

Observing the given graph, we can see that the line passes through the points $(2,1)$ and $(5,3).$ Let's mark these in the diagram.

We can use the points to determine the run and the rise of the line. The run is the horizontal distance between the points and the rise is the vertical distance between them. Let's find these distances in the graph.

We can now find the slope, $m,$ of the line using the formula $m=\frac{\text{rise}}{\text{run}}.$ $m=\dfrac{\text{rise}}{\text{run}} \quad \Rightarrow \quad m=\dfrac{\text{2}}{\text{3}}$ Thus, the slope is $m=\frac{2}{3}.$

b

The graph we have been given passes through the points $(\text{-}2,15)$ and $(4,3).$ Let's mark these in the diagram.

Next we need to find the run and the rise using these points. We can see it as moving from one point to the other by taking a horizontal step followed by a vertical. The run is the horizontal step and the rise is the vertical. Since the vertical step we need to take is down the rise will be negative.

The slope of the line we can now find by dividing the rise by the run $m=\dfrac{\text{rise}}{\text{run}} \quad \Rightarrow \quad m=\dfrac{\text{-} 12}{6}=\text{-} 2$ Thus, the slope is $m=\text{-} 2.$