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Consider the four points π΄: one, two; π΅: six, zero; πΆ: negative one, negative two; and π·: three, negative four.
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Part one: Work out the slope of the line π΄π΅.
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Part two: Work out the slope of the line πΆπ·.
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Part three: Are the two lines parallel?
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The slope of any line can be calculated by using the formula: π¦ two minus π¦ one divided by π₯ two minus π₯ one.
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This is the change in the π¦-coordinates divided by the change in the π₯-coordinates.
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Letβs first consider the slope of π΄π΅, where π΄ has coordinates one, two and π΅ has coordinates six, zero.
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Substituting these values into the formula gives us zero minus two divided by six minus one.
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Zero minus two is equal to negative two.
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And six minus one is equal to five.
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Therefore, the slope of the line π΄π΅ is negative two-fifths.
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Letβs now consider the slope of πΆπ·, where πΆ has coordinates negative one, negative two and π· has coordinates three, negative four.
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Substituting these values into the formula gives us negative four minus negative two divided by three minus negative one.
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Minus four minus negative two is the same as minus four plus two.
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And minus four plus two is equal to negative two.
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On the denominator, three minus negative one is the same as three plus one.
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Three plus one is equal to four.
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Therefore, the slope of the line πΆπ· is minus two divided by four.
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This fraction can be simplified to give us the slope of the line πΆπ· as negative one-half.
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The third part of our question asked if the two lines, π΄π΅ and πΆπ·, are parallel.
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Well, parallel lines have the same slope or gradient.
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So we need to consider whether negative two-fifths is the same as negative a half.
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Well, clearly these two fractions are different.
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Therefore, the lines π΄π΅ and πΆπ· are not parallel to each other.