A line passes through (5 ,6 )(5,6) and (7 ,3 )(7,3). A second line passes through (2 ,8 )(2,8). What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Somebody N.
May 16, 2018

color(blue)((1,19/2)(1,192)

Explanation:

First we need to find the equation of the line that passes through the points (5,6) and (7,3)(5,6)and(7,3)

Using point slope form of a line:

(y_2-y_1)=m(x_2-x_1)(y2−y1)=m(x2−x1)

Where mm is the gradient.

m=(y_2-y_1)/(x_2-x_1)=(6-3)/(5-7)=-3/2m=y2−y1x2−x1=6−35−7=−32

y-3=-3/2(x-7)y−3=−32(x−7)

y=-3/2x+27/2y=−32x+272

The line passing through point (2,8)(2,8) has to be parallel to the line we just found. If two lines are parallel, then they have the same gradients.

Using point slope form of a line:

y-8=-3/2(x-2)y−8=−32(x−2)

y=-3/2x+11y=−32x+11

To find another point that this line passes through, we just plug in a value for xx and calculate the corresponding value of yy

x=1x=1

y=-3/2(1)+11=19/2y=−32(1)+11=192

So (1,19/2)(1,192) in another point.

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