A line passes through $(5, 8)$ $(5 ,8 )$ 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 · 2016-09-11T10:36:59

For 2 lines to be parallel, they need to have the same slope

Get the slope of the first line

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

$m = \frac{8 - 9}{5 - 7}$ $m = (8 - 9)/(5 - 7)$

$\Rightarrow m = \frac{1}{2}$ $=> m = 1/2$

Now get the equation of the 2nd line

$y = m x + b$ $y = mx + b$

$6 = (\frac{1}{2}) 3 + b$ $6 = (1/2)3 + b$

$\Rightarrow 12 = 3 + 2 b$ $=> 12 = 3 + 2b$

$b = \frac{9}{2}$ $b = 9/2$

Hence, the equation of the 2nd line is

$y = \frac{1}{2} x + \frac{9}{2}$ $y = 1/2x + 9/2$

To find another point that the line passes through, simply substitute any value of $x$ $x$ (or $y$ $y$ ) and solve for the value of the other

A line passes through (5 ,8 )(5,8)(5 ,8 ) 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?