Question Video: Finding the Slopes of Lines and Using Them to Determine If the Lines Are Parallel | Nagwa Question Video: Finding the Slopes of Lines and Using Them to Determine If the Lines Are Parallel | Nagwa

# Question Video: Finding the Slopes of Lines and Using Them to Determine If the Lines Are Parallel Mathematics • Third Year of Preparatory School

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Line πΏ passes through points (β1, 2) and (2, 3), and line π passes through points (β1, β1) and (5, 1). Work out the slope of line πΏ. Work out the slope of line π. Are these two lines parallel?

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### Video Transcript

Line πΏ passes through points negative one, two and two, three, and line π passes through points negative one, negative one and five, one. Work out the slope of line πΏ. Work out the slope of line π. Are these two lines parallel?

We have two lines, line πΏ and line π. The first thing weβre asked for is the slope of both of these lines. The slope is the changes in π¦ over the changes in π₯. If we have two points, we can find the slope by subtracting π¦ two minus π¦ one and putting that over π₯ two minus π₯ one.

For line πΏ, we have our two points. We can label the first point π₯ one, π¦ one and the second point π₯ two, π¦ two. π¦ two minus π¦ one equals three minus two. And π₯ two minus π₯ one is two minus negative one. Three minus two is one. Two minus negative one equals three. The slope of line πΏ is one-third.

Weβll follow the same process for line π. We take the two points. Weβll call the first point π₯ one, π¦ one and the second π₯ two, π¦ two. π¦ two minus π¦ one is one minus negative one over π₯ two minus π₯ one, five minus negative one. One minus negative one is two. Five minus negative one is six.

We can reduce the fraction two-sixths. If we divide the numerator and the denominator by two, two-sixths is reduced to one-third. The slope of line π is also one-third.

The last question is, are the two lines parallel? We remember that parallel lines have the same slope. Since line πΏ and line π have the same slope, they are parallel lines.

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