A line passes through $(4 ,7 )$ and $(6 ,4 )$ . A second line passes through $(3 ,5 )$ . 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 · 2018-06-23T06:17:13

$color(crimson)("One other point on the second line is " (3, 5)$

$"Slope of line 1 " = m = (y_2 - y_1) / (x_2 - x_1) = (4-7) / (6-4) = -3/2$

![https://math.tutorvista.com/geometry/http://distance-between-lines.html](https://useruploads.socratic.org/QH6H3aLYSWuXO6pacjwH_parallel-lines.png)

As $2^(nd)$ line is parallel to the first line, slope of second line also $-3/2$

#"Equation of second line in point - slope form is "

$(y - 5) = -3/2 * (x - 3)$

$2y - 10 = -3x + 9$

$3x + 2y = 19$

Let y = 5. Then x = 3#

$color(crimson)("One other point on the second line is " (3, 5)$

A line passes through (4 ,7 )(4 ,7 ) and (6 ,4 )(6 ,4 ). A second line passes through (3 ,5 )(3 ,5 ). What is one other point that the second line may pass through if it is parallel to the first line?