A line passes through (5 ,8 )(5,8) and (2 ,9 )(2,9). 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?

1 Answer
marfre
Apr 20, 2018

There are many answers based on the selected xx value.
One answer is (6, 4)(6,4)

Explanation:

Given: two parallel lines: "line"_1 (5, 8), (2, 9); " " "line"_2 (3,5)line1(5,8),(2,9); line2(3,5)

Find the slope of "line"_1line1:
m = (y_2 - y_1)/(x_2 - x_1) = (9 - 8)/(2 - 5) = 1/-3 = -1/3m=y2−y1x2−x1=9−82−5=1−3=−13

Parallel lines have the same slope.

Find the equation of the second line using the given point: y - y_1 = m(x - x_1)y−y1=m(x−x1)

y - 5 = -1/3 (x - 3)y−5=−13(x−3)

Simplify by using distribution and adding 55 to both sides:
y - 5 = -1/3x + (-1/3)(-3/1)y−5=−13x+(−13)(−31)

y - 5 = -1/3x + 1y−5=−13x+1

y = -1/3x + 6y=−13x+6

To get another point, just plug in any xx value.

Let x = 6; y = -1/3 * 6/1 + 6 = -2 + 6 = 4; " "(6, 4)x=6;y=−13⋅61+6=−2+6=4; (6,4)

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