$\"\"$

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a.

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Let the line $\"\"$ passing through the points $\"\"$ and $\"\"$ .

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Redraw the given diagram.

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$\"\"$

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Observe the above diagram :

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Opposite side of $\"\"$ is $\"\"$ .

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Adjacent side of $\"\"$ is $\"\"$ .

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Slope of the line $\"\"$ : $\"\"$ .

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$\"\"$

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Definition of tangent ratio : $\"\"$ .

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$\"\"$ .

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Therefore, the slope $\"\"$ of the line $\"\"$ is $\"\"$ .

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$\"\"$

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b.

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From part a, we know that the slope of a line is equivalent to the tangent of its angle of inclination.

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Therefore, $\"\"$ and $\"\"$ .

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The angle formed by the intersection of the two lines $\"\"$ is equivalent to $\"\"$

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Use this information to derive a formula for $\"\"$ .

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$\"\"$ (Since $\"\"$ )

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Apply tangent difference identity : $\"\"$ .

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$\"\"$

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$\"\"$

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c.

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The two lines are $\"\"$ and $\"\"$ .

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Compare the lines with slope intercept form $\"\"$ , where $\"\"$ is slope and $\"\"$ is y - intercept.

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Slopes of the lines $\"\"$ and $\"\"$ .

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Angle between the lines : $\"\"$ .

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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The angle between the lines $\"\"$ and $\"\"$ is $\"\"$ .

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$\"\"$

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a.

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The slope $\"\"$ of the line $\"\"$ is $\"\"$ .

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b.

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$\"\"$ .

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c.

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The angle between the lines $\"\"$ and $\"\"$ is $\"\"$ .