A line passes through (2 ,3 )(2,3) and ( 4, 5 )(4,5). A second line passes through ( 7, 4 )(7,4). What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
smendyka
Mar 14, 2018

See a solution process below:

Explanation:

First, we need to determine the slope of the first line. The slope can be found by using the formula: m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))m=y2−y1x2−x1

Where mm is the slope and (color(blue)(x_1, y_1)x1,y1) and (color(red)(x_2, y_2)x2,y2) are the two points on the line.

Substituting the values from the points in the problem gives:

m = (color(red)(5) - color(blue)(3))/(color(red)(4) - color(blue)(2)) = 2/2 = 1m=5−34−2=22=1

Because the problem states the two lines are parallel therefore the second line will have the same slope of m = 1m=1

Because we have a slope and one point for the second line we can write an equation for the line using the point-slope formula. The point-slope form of a linear equation is: (y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))(y−y1)=m(x−x1)

Where (color(blue)(x_1), color(blue)(y_1))(x1,y1) is a point on the line and color(red)(m)m is the slope.

Substituting the values from the point in the problem and slope we calculated gives:

(y - color(blue)(4)) = color(red)(1)(x - color(blue)(7))(y−4)=1(x−7)

y - color(blue)(4) = x - color(blue)(7)y−4=x−7

y - color(blue)(4) + 4 = x - color(blue)(7) + 4y−4+4=x−7+4

y - 0 = x - 3y−0=x−3

y = x - 3y=x−3

To find another point on this second line substitute any number you want for xx (other than 7) and calculate yy.

I am going to choose an easy number - 00

y = x - 3y=x−3 becomes:

y = 0 - 3y=0−3

y = -3y=−3

So the point would be: (0, -3)(0,−3)

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