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Determining the Slope of a Line

Determining the Slope of a Line 1.9 - Solution

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In the lyrics of We Will Graph You we can find some information regarding the line we want to draw. The words a line is 44 when xx is nil we read as y=4y=4 when x=0.x=0. Therefore, the graph has its yy-intercept at y=4.y=4. We have now found one point on the graph.

The next line, and decrease to 22 when xx is 33, gives us another point on the line, (3,2).(3,2). Let's mark this point in the diagram as well.

Next Brian tells us to draw the graph. We will, we will graph it by connecting the points with a line.

Brian May next puts us under pressure to find the slope of this line. But we are champions so we go ahead and present a formula that will help us calculate the slope . m=ΔyΔx m=\dfrac{\Delta y}{\Delta x} The points we used when we drew the line can be helpful in finding Δy\Delta y and Δx.\Delta x.

We will now substitute -2\text{-} 2 and 33 for Δy\Delta y and Δx\Delta x in the formula and, like a kind of magic, we find the slope. m=ΔyΔxm=-23=-23 m=\dfrac{\Delta y}{\Delta x} \quad \Rightarrow \quad m=\dfrac{\text{-} 2}{3}=\text{-} \dfrac{2}{3} The final line before the chorus tells us to find its xx and yy-intercepts. We already know the yy-intercept, (0,4).(0, 4). The x-x\text{-}intercept we can identify by looking at the graph.

The line intercepts the x-x\text{-}axis at (6,0).(6,0). Therefore, the x-x\text{-}intercept is 6.6. Let's summarize what we have found about this graph. Slope: m=-23x-intercept: (6,0)y-intercept: (0,4)\begin{aligned} \text{Slope: } & m=\text{-} \dfrac{2}{3} \\ x\text{-intercept: } & (6,0) \\ y\text{-intercept: } & (0,4) \end{aligned}