A line passes through $(3, 4)$ $(3 ,4 )$ and $(4, 7)$ $(4 ,7 )$ . A second line passes through $(7, 9)$ $(7 ,9 )$ . 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 $(3, 4)$ $(3 ,4 )$ and $(4, 7)$ $(4 ,7 )$ . A second line passes through $(7, 9)$ $(7 ,9 )$ . 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 · 2018-01-26T06:37:22

Any point on the line $y = 3 x - 12$ $y = 3x-12$ is a viable answer.

Explanation:

Slope formula from two points:

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m = (y_2-y_1)/(x_2-x_1)$

Slope of the given line:

$m = \frac{7 - 4}{4 - 3} = \frac{3}{1} = 3$ $m = (7-4)/(4-3)=3/1=3$

The equation of this line using point-slope form:

$y - y_{1} = m (x - x_{1}) \Rightarrow$ $y-y_1=m(x-x_1)=>$

$y - 7 = 3 (x - 4)$ $y-7=3(x-4)$

$y - 7 = 3 x - 12$ $y-7=3x-12$

$y = 3 x - 5$ $y=3x-5$

Since the unknown line is parallel to this one, it has the same slope. Using the newfound slope, we can craft an equation for the new line:

$y - y_{1} = m (x - x_{1}) \Rightarrow$ $y-y_1=m(x-x_1)=>$

$y - 9 = 3 (x - 7)$ $y-9=3(x-7)$

$y - 9 = 3 x - 21$ $y-9=3x-21$

$y = 3 x - 12$ $y=3x-12$

This is the "second line" that the question mentions. Now, we just need to pick a point anywhere on this line by plugging in an $x$ $x$ -value and get a $y$ $y$ -value back. I'll pick 6 for an $x$ $x$ -value:

$y = 3 x - 12 \Rightarrow$ $y=3x-12=>$

$y = 3 (6) - 12$ $y=3(6)-12$

$y = 18 - 12$ $y=18-12$

$y = 6$ $y=6$

A point on the line is $(6, 6)$ $(6, 6)$ .

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A line passes through $(3, 4)$ $(3 ,4 )$ and $(4, 7)$ $(4 ,7 )$ . A second line passes through $(7, 9)$ $(7 ,9 )$ . 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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Impact of this question

Science

Math

Humanities

... and beyond

A line passes through (3,4)(3 ,4 ) and (4,7)(4 ,7 ). A second line passes through (7,9)(7 ,9 ). 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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Impact of this question

A line passes through $(3, 4)$ $(3 ,4 )$ and $(4, 7)$ $(4 ,7 )$ . A second line passes through $(7, 9)$ $(7 ,9 )$ . What is one other point that the second line may pass through if it is parallel to the first line?