Video Transcript
Write the equation represented
by the graph shown. Give your answer in the form 𝑦
equals 𝑚𝑥 plus 𝑏.
So we have a diagram of a
straight line. And we’re asked to give its
equation in slope-intercept form, which means we need to work out what each of
these two things are. From looking at the diagram, we
can see that the 𝑦-intercept is negative four, which means that the value of
𝑏, which is the letter used here to represent the 𝑦-intercept, must be
negative four. So I can write down the
beginnings of the equation of this straight line; it’s 𝑦 equals 𝑚𝑥 minus
four. Next, we need to find the value
of 𝑚, the slope of this line. And in order to do this, I need
the coordinates of two points that lie on the line.
We’ve already had identified
one point, the point with coordinates zero, negative four. Looking at the graph, I can
also see that there’s a point here that would be convenient to use. This point lies on the 𝑥-axis
and has the coordinates six, zero. So I’m going to use these two
points to calculate the slope of the line. So, the slope of the line can
be calculated as a change in 𝑦 divided by a change in 𝑥. Or you can think of this as 𝑦
two minus 𝑦 one over 𝑥 two minus 𝑥 one, if you choose to label the two points
as 𝑥 one, 𝑦 one and 𝑥 two, 𝑦 two. I’m just going to look at the
diagram in order to work out the change in 𝑦 and the change in 𝑥.
The change in 𝑦 first of all
then, well that is the vertical length in this triangle. And I can see that it moves
from a 𝑦-coordinate of negative four to a 𝑦-coordinate of zero. Therefore, the change in 𝑦 is
positive four. Now, let’s look at the change
in 𝑥; this is the horizontal change. So I can see from the diagram
that this moves from a value of zero to a value of six, which gives me a change
in 𝑥 of positive six. So the slope of this line then
is four over six. But this can be written as a
simplified fraction; it’s two-thirds. Finally then, I just need to
substitute this value of 𝑚, the slope of the line, into the equation. So the equation of the line
represented by this graph is 𝑦 equals two-thirds 𝑥 minus four.
