A line passes through $(5, 0)$ $(5 ,0 )$ and $(7, 9)$ $(7 ,9 )$ . A second line passes through $(3, 6)$ $(3 ,6 )$ . What is one other point that the second line may pass through if it is parallel to the first line?

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A line passes through $(5, 0)$ $(5 ,0 )$ and $(7, 9)$ $(7 ,9 )$ . A second line passes through $(3, 6)$ $(3 ,6 )$ . What is one other point that the second line may pass through if it is parallel to the first line?

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Answer 1 · 2017-12-22T15:18:41

$(2, \frac{3}{2})$ $(2,3/2)$

Explanation:

$establish the equation of the parallel line$ $"establish the equation of the parallel line"$

$the equation of a line in slope-intercept form$ $"the equation of a line in "color(blue)"slope-intercept form "$ is.

$∙ x y = m x + b$ $•color(white)(x)y=mx+b$

$where m is the slope and b the y-intercept$ $"where m is the slope and b the y-intercept"$

$to calculate m use the gradient formula$ $"to calculate m use the "color(blue)"gradient formula"$

$color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))$

$"let "(x_1,y_1)=(5,0)" and "(x_2,y_2)=(7,9)$

$rArrm=(9-0)/(7-5)=9/2$

$• " parallel lines have equal slopes"$

$rArr"slope of parallel line "=9/2$

$rArry=9/2x+b color(blue)" is the partial equation"$

$"to find b substitute "(3,6)" into the partial equation"$

$6=27/2+brArrb=-15/2$

$rArry=9/2x-15/2larrcolor(blue)"equation of parallel line"$

$"choose any value for x and substitute into the equation"$

$x=2toy=9-15/2=3/2$

$"another point on the line is "(2,3/2)$

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A line passes through $(5, 0)$ $(5 ,0 )$ and $(7, 9)$ $(7 ,9 )$ . A second line passes through $(3, 6)$ $(3 ,6 )$ . What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer

Explanation:

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Science

Math

Humanities

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A line passes through (5 ,0 )(5,0)(5 ,0 ) and (7 ,9 )(7,9)(7 ,9 ). A second line passes through (3 ,6 )(3,6)(3 ,6 ). What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer

Explanation:

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A line passes through $(5, 0)$ $(5 ,0 )$ and $(7, 9)$ $(7 ,9 )$ . A second line passes through $(3, 6)$ $(3 ,6 )$ . What is one other point that the second line may pass through if it is parallel to the first line?