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Question

What is the value of $$y$$ so that the line through $$( 3 , y )$$ and $$( 2,7 )$$ is parallel to the line through $$( - 1,4 )$$ and $$( 0,6 ) ?$$


Solution

Slope of $$(0, 6)$$ and $$(-1, 4)$$ is
$$\dfrac{6-4}{0+1}=\dfrac{2}{1}=2$$
Slope of $$(3, y)$$ and $$(2, 7)$$
$$=\dfrac{y-7}{3-2}=y-7$$
Since the lines are parallel, we have $$y-7=2$$
$$\Rightarrow y=9$$.

1216026_1314136_ans_257e58cee2784ea5b5c1a75e73431e6e.jpg

Mathematics

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