### Video Transcript

Which of the following is the
function represented by the shown graph? Option A, π¦ equals three-halves π₯
plus two. Option B, π¦ equals two π₯ plus
two-thirds. Option C, π¦ equals two-thirds π₯
minus two. Option D, π₯ equals two-thirds π¦
plus two. Or option E, π¦ equals two-thirds
π₯ plus two.

Letβs recall that the general form
of a linear equation is π¦ equals ππ₯ plus π or π¦ equals ππ₯ plus π, where the
constant term of π or π represents the π¦-intercept of the function. The value of π will indicate the
slope or gradient of the line. So therefore, if we were to
calculate the slope and the π¦-intercept of this drawn function, we could work out
what the function is. We can recall that, between two
coordinates π₯ one, π¦ one and π₯ two, π¦ two, the slope is equal to π¦ two minus π¦
one over π₯ two minus π₯ one.

We can select any two coordinates
on the line for π₯ one, π¦ one and π₯ two, π¦ two. But often the easiest ones to pick
are those which have integer values. We can see here that zero, two and
three, four both lie on the line. It doesnβt matter which coordinate
we designate as π₯ one, π¦ one and which we designate as π₯ two, π¦ two. To find the slope, we substitute in
our π¦ two and π¦ one values to give us four minus two over the π₯ two minus π₯ one
values, which is three minus zero. Simplifying this, we have a slope
of two-thirds.

To find the π¦-intercept, we look
at the graph to see where it crosses the π¦-axis. And that happens when the π¦-value
is two. We can then fill in our values of
slope and π¦-intercept into the general equation. We found that the slope π is equal
to two-thirds and the π¦-intercept of π is equal to two. And so our answer is that given in
option E, π¦ equals two-thirds π₯ plus two.