Video: Pack 1 • Paper 1 • Question 6

Pack 1 • Paper 1 • Question 6

02:14

Video Transcript

A line 𝐿 one has equation 𝑦 equals two 𝑥 minus five and a line 𝐿 two has equation two 𝑦 plus four 𝑥 equals minus seven or negative seven. Determine whether the two lines are perpendicular.

Two lines are perpendicular if 𝑚 one multiplied by 𝑚 two is equal to minus one if their gradients multiply together to give us an answer of minus one. 𝐿 one, 𝑦 equals two 𝑥 minus five, is already written in the form 𝑦 equals 𝑚𝑥 plus 𝑐, where 𝑚 is the gradient and 𝑐 is the 𝑦-intercept. This means that the gradient of 𝐿 one is equal to two. 𝑚 one is equal to two.

In order to work out the gradient of 𝐿 two, we need to make 𝑦 the subject of the equation so that it is in the form 𝑦 equals 𝑚𝑥 plus 𝑐. Subtracting four 𝑥 from both sides of the equation gives us two 𝑦 is equal to minus four 𝑥 minus seven. Dividing both sides of this equation by two gives us 𝑦 is equal to minus two 𝑥 minus seven over two or minus 3.5. The gradient of 𝐿 two is, therefore, minus two.

We know that two lines are perpendicular if 𝑚 one multiplied by 𝑚 two is equal to minus one. In this case, 𝑚 one was equal to two and 𝑚 two was equal to minus two. Two multiplied by minus two is equal to minus four. As the two gradients do not have a product of minus one, they are not perpendicular.

The lines 𝐿 one, 𝑦 equals two 𝑥 minus five, and 𝐿 two, two 𝑦 plus four 𝑥 equals minus seven, are not perpendicular.

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