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

Line 𝐿 passes through points (βˆ’1, 2) and (2, 3), and line 𝑀 passes through points (βˆ’1, βˆ’1) and (5, 1). Work out the slope of line 𝐿. Work out the slope of line 𝑀. Are these two lines parallel?

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Video Transcript

Line 𝐿 passes through points negative one, two and two, three, and line 𝑀 passes through points negative one, negative one and five, one. Work out the slope of line 𝐿. Work out the slope of line 𝑀. Are these two lines parallel?

We have two lines, line 𝐿 and line 𝑀. The first thing we’re asked for is the slope of both of these lines. The slope is the changes in 𝑦 over the changes in π‘₯. If we have two points, we can find the slope by subtracting 𝑦 two minus 𝑦 one and putting that over π‘₯ two minus π‘₯ one.

For line 𝐿, we have our two points. We can label the first point π‘₯ one, 𝑦 one and the second point π‘₯ two, 𝑦 two. 𝑦 two minus 𝑦 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 𝐿 is one-third.

We’ll follow the same process for line 𝑀. We take the two points. We’ll call the first point π‘₯ one, 𝑦 one and the second π‘₯ two, 𝑦 two. 𝑦 two minus 𝑦 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 𝑀 is also one-third.

The last question is, are the two lines parallel? We remember that parallel lines have the same slope. Since line 𝐿 and line 𝑀 have the same slope, they are parallel lines.

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