Question Video: Determining Which Point Satisfies a Given Linear Function

Which of the following set of coordinates lies on 𝑓(𝑥) = −19𝑥 − 16? [A] (10, −16) [B] (10, −206) [C] (−206, 10) [D] (−206, −16)

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Video Transcript

Which of the following set of coordinates lies on 𝑓 of 𝑥 is equal to negative 19𝑥 minus 16? Is it (A) 10, negative 16; (B) 10, negative 206; (C) negative 206, 10; or (D) negative 206, negative 16?

We are used to any pair of coordinates being written in the form 𝑥, 𝑦. The first coordinate is the 𝑥-value, and the second is the 𝑦-value. The function 𝑓 of 𝑥 is equal to negative 19𝑥 minus 16 is the same as 𝑦 equals negative 19𝑥 minus 16. As 𝑦 and 𝑓 of 𝑥 are interchangeable, we can write the coordinate pair as 𝑥, 𝑓 of 𝑥. The first value is known as the input and the second value the output.

We need to work out which of the four options satisfies the function. We notice that both option (A) and option (B) have an input or 𝑥-value of 10. This means that in order to calculate the output, we need to work out 𝑓 of 10. Substituting in 𝑥 equals 10 gives us negative 19 multiplied by 10 minus 16. Multiplying a negative number by a positive gives a negative answer. So negative 19 multiplied by 10 is negative 190. Subtracting 16 from this gives us negative 206. This means that the coordinate pair 10, negative 206 lies on the function. As option (A) was 10, negative 16, this is incorrect. Option (B), on the other hand, was 10, negative 206. So this is the correct answer.

We could check to see if options (C) and (D) are correct by substituting negative 206 in for 𝑥. 𝑓 of negative 206 is equal to negative 19 multiplied by negative 206 minus 16. We can clearly see that this will not satisfy either of our options, as our value is too large. An input of negative 206 gives an output of 3898. The coordinate pair negative 206, 3898 lies on the function. This does not correspond to option (C) or (D). So these are both incorrect. The correct answer is option (B).

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