Video Transcript
Two lines have slopes of six-fifths and twelve-tenths and cut the 𝑦-axis at different points. Are the two lines parallel?
In order to answer this question, we begin by recalling our definition of parallel lines. We know that two lines are parallel if they are the same distance apart and never intersect. The two lines could have positive or negative slope as shown. Alternatively, they could both be horizontal or both vertical. Any two parallel lines must therefore have the same slope or gradient. In this question, we are told that two lines have slopes of six-fifths and twelve-tenths. We will call these slopes or gradients 𝑚 sub one and 𝑚 sub two, respectively.
In order to find out whether the two lines are parallel, we need to work out whether our two fractions are equivalent. Both the numerator and denominator of our second fraction are even. So we can therefore divide the top and bottom by two. 12 divided by two is equal to six, and 10 divided by two is equal to five. The fraction twelve-tenths is therefore equal to the fraction six-fifths.
This means that the slopes, or gradients, of the two lines are equal. And since the two lines cut the 𝑦-axis at different points, they are not coincident, where coincident lines are lines that lie on top of one another. We can therefore conclude that the correct answer is yes, the two lines are parallel.
