### Video Transcript

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

The first part of the question
asked us to fill in the table by calculating the value of 𝑦 or 𝑓 of 𝑥 when 𝑥
equals negative two, when 𝑥 equals zero, and when 𝑥 equals two. When 𝑥 is equal to negative two,
𝑓 of 𝑥 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 𝑥 is equal to zero, 𝑓 of 𝑥
or 𝑦 is equal to negative two multiplied by zero plus five. This is equal to five. Therefore, when 𝑥 equals zero, 𝑓
of 𝑥 equals five.

Finally, when 𝑥 is equal to two,
𝑓 of 𝑥 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 𝑥 plus five.

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