Determine whether the distinct lines through each pair of points are parallel. (2,4) and (6,1) ;

Determine whether the distinct lines through each pair of...

Key Concepts

Parallel lines

Parallel lines are defined as lines in the same plane that never intersect. They share the same slope, which is the key criterion used to determine if two lines are parallel, irrespective of their y-intercepts.

Line through two points

In analytic geometry, any two distinct points determine a unique line, leading to the formulation of its equation. This concept serves as the basis for identifying lines and understanding how they are represented in a coordinate system.

Slope

The slope of a line measures its steepness and direction by calculating the ratio of the vertical change to the horizontal change between any two points on the line. It is a fundamental property used to describe linear relationships in the coordinate plane.

Transcript

00:02 For this problem, we are asked to tell if the lines that are drawn between each pair of points are parallel to one another.

00:13 Now, one way that you could do this is to plot this pair of points right here.

00:18 We'll call this line one.

00:20 We could plot that pair of points and draw a line between them.

00:24 And then we could plot this pair of points and draw a line two between them.

00:30 And we could just simply see if the lines were parallel.

00:34 That's not a great way to do it because they could look parallel, but actually be not quite parallel, and we just couldn't visually see that.

00:43 A better way to do that is to use the formula, m is equal to the change in y over the change in x, and see if the two lines have the same slope, because lines that are parallel always have the same slope.

01:04 So we need to assign this the value of x1 and y1, and this the value of x2 and y2, and we need to assign this the value of x1 and y1, and this the value of x2 and y2.

01:28 And we're going to go through and we're going to solve this equation right here twice, once for line one and then once for line two.

01:37 And we're going to see if we have the same exact slope each time.

01:42 So let's do the first line.

01:45 We'll do it in blue.

01:49 And i'm going to simply substitute those values in y2 is 1 minus 4 over x2 is 6 minus x1 is 2...

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