verify parallelismVerify if the line through (-1,1) and (5,2) is parallel to the line through (-1,4) and (2,3)?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

Two straight lines are parallel if the slope of both of them is the same. The slope of a line passing through (x1, y1) and (x2, y2) is given by (y2 - y1)/(x2 - x1)

Here we have line passing through (-1,1) and (5,2), and through (-1,4) and (2,3).

The slope of the line through (-1,1) and (5,2) is (2 -1)/(5+1) = 1/6

That of the line through (-1,4) and (2,3) is ( 4 - 3)/(-1 -2) = -1/3

As the slope is not the same, the lines are not parallel.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Since we know the points through the lines are passing, we'll calculate the slopes.

Slope of line through the points  (-1,1) and (5,2) is:

m1= (y2-y1)/(x2-x1)

x1=-1,y1=1,x2=5,y2=2

m1 = (2-1)/(5+1)

m1 = 1/6

Now, we'll consider the next two points (-1,4) and (2,3).

m2 = (3-4)/(2+1)

m2 = 1/3

We know that 2 lines are parallel if their slopes are equal.

m1 is different from m2.

Therefore, the given lines are not parallel.

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