A line passes through $(3, 4)$ $(3 ,4 )$ and $(4, 7)$ $(4 ,7 )$ . A second line passes through $(7, 3)$ $(7 ,3 )$ . 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 $(7, 3)$ $(7 ,3 )$ . 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 · 2017-07-27T12:06:37

See a solution process below:

Explanation:

First, we need to calculate the slope of the first line: $m_{1}$ $m_1$ . The slope can be found by using the formula: $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))$

Where $m$ $m$ is the slope and ( $x_{1}, y_{1}$ $color(blue)(x_1, y_1)$ ) and ( $x_{2}, y_{2}$ $color(red)(x_2, y_2)$ ) are the two points on the line.

Substituting the values from the points in the problem gives:

$m_{1} = \frac{7 - 4}{4 - 3} = \frac{3}{1}$ $m_1 = (color(red)(7) - color(blue)(4))/(color(red)(4) - color(blue)(3)) = 3/1$

Because the two lines are parallel, the slope of the second line will also be $\frac{3}{1}$ $3/1$ . We can call the slope of the second line $m_{2}$ $m_2$

Substituting the values from the one point and the slope we calculated for the first line gives:

$m_{2} = \frac{y - 3}{x - 7}$ $m_2 = (color(red)(y) - color(blue)(3))/(color(red)(x) - color(blue)(7))$

$\frac{3}{1} = \frac{y - 3}{x - 7}$ $3/1 = (color(red)(y) - color(blue)(3))/(color(red)(x) - color(blue)(7))$

We can now solve these two equations to get another point on the second line:

- Solve for the Numerator:

$y - 3 = 3$ $y - 3 = 3$

$y - 3 + 3 = 3 + 3$ $y - 3 + color(red)(3) = 3 + color(red)(3)$

$y - 0 = 6$ $y - 0 = 6$

$y = 6$ $y = 6$

- Solve for the Denominator:

$x - 7 = 1$ $x - 7 = 1$

$x - 0 = 8$ $x - 0 = 8$

One other point on the second line is: $(8, 6)$ $(8, 6)$

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