Video: Graphing Linear Functions by Making Tables

Consider the function 𝑓(π‘₯) = βˆ’2π‘₯ + 5. Fill in the table. Identify the three points that lie on the line 𝑦 = βˆ’2π‘₯ + 5.

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Video Transcript

Consider the function 𝑓 of π‘₯ equals negative two π‘₯ plus five. Fill in the table. Identify the three points that lie on the line 𝑦 equals negative two π‘₯ plus five.

The first part of the question asked us to fill in the table by calculating the value of 𝑦 or 𝑓 of π‘₯ when π‘₯ equals negative two, when π‘₯ equals zero, and when π‘₯ equals two. When π‘₯ is equal to negative two, 𝑓 of π‘₯ is equal to negative two multiplied by negative two plus five. This is equal to nine as negative two multiplied by negative two is four and four plus five is equal to nine.

When π‘₯ is equal to zero, 𝑓 of π‘₯ or 𝑦 is equal to negative two multiplied by zero plus five. This is equal to five. Therefore, when π‘₯ equals zero, 𝑓 of π‘₯ equals five.

Finally, when π‘₯ is equal to two, 𝑓 of π‘₯ is equal to negative two multiplied by two plus five. This is equal to one as negative two multiplied by two is negative four and negative four plus five is equal to one.

This means that the three missing numbers from the table were nine, five, and one respectively. We can go one stage further by saying that negative two, nine; zero, five; and two, one lie on the line 𝑦 equals negative two π‘₯ plus five.

These three coordinates correspond to point 𝐴, point 𝐢, and point 𝐸 on the diagram. The straight line that passes through these points will have equation 𝑦 equals negative two π‘₯ plus five.

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