A line passes through (4 ,3 ) and (2 ,9 ). A second line passes through (7 ,1 ). What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Jun 6, 2018

From the slope and the given point, we can determine many points that will make this line parallel, including: (6,4)

Explanation:

For the lines to be parallel, it implies that they have the same slope. So, let's first determine what is that slope.
For the first line we have 2 points, so we can determine the slope of that line as:
m = (Delta y)/(Delta x) = (y_2-y_1)/(x_2-x_1) = (9-3)/(2-4) = 6/-2 = -3

The slope of the other line must be the same: m=-3
As stated in the question, the line goes through point (7,1). Let's call that point P_1.
For our second point, P_2, we can choose any value for x_2, but we need to determine the corresponding value for y_2.
So, if we choose, say, x_2=6, what is the value of y_2 ?
We can apply the same equation for slope, and our only unknown is y_2:
m = (Delta y)/(Delta x) = (y_2-y_1)/(x_2-x_1)
-3= (y_2 - 1)/(6-7)
-3= (y_2-1)/-1
3 = y_2-1,
y_2 = 4
So, a valid point in that parallel line is (6,4)

There is an infinite number of possible solutions, as long as we maintain m=-3. Another example would be (8,-2)