### Video Transcript

Find the equation of the straight
line that passes through the origin and the point of intersection of the two
straight lines π₯ equals negative seventeen-fourths and π¦ equals negative five.

If we sketch in an π₯π¦-coordinate
plane, then we can draw in this given straight line π₯ equals negative
seventeen-fourths β this is a vertical line crossing the π₯-axis at negative
seventeen-fourths β and also the straight line π¦ equals negative five β that would
be a horizontal line that crosses the π¦-axis at negative five. The straight line whose equation we
want to solve for passes through the point of intersection of these two lines, and
it also passes through the origin. So itβs this pink line then whose
equation we want to find.

As we think of the equation of a
straight line, there are different ways of writing this expression. The way weβll use is to say that
the π¦-coordinate of the line is equal to the slope π of the line multiplied by the
π₯-value plus this value π, which is the π¦-intercept of the line, the place where
it crosses the π¦-axis. If π¦ equals ππ₯ plus π, itβs π
and π that we want to find. And letβs start by solving for the
slope π of this pink line here.

The slope π is equal to the
difference in the π¦-coordinates of two points on a given line divided by the
difference in the π₯-coordinates of those corresponding points. In our scenario, two points on the
line are first this point of intersection with coordinates negative
seventeen-fourths, negative five and then second the origin with coordinates zero,
zero.

If we consider these points from
left to right so that this point of intersection is our first point and the origin
is our second, then we write that π¦ two, thatβs zero, minus π¦ one, thatβs negative
five, divided by π₯ two, thatβs also zero, minus π₯ one, thatβs negative
seventeen-fourths, is equal to the slope π. This equals five over
seventeen-fourths or, if we multiply top and bottom by four, twenty
seventeenths. This is the slope π of our
line.

We can update our expression then
for the equation of our straight line. Itβs π¦ equals twenty seventeenths
π₯ plus π. Like we said, this value π is the
π¦-intercept of the line. And we notice now that since this
line passes through the origin, the π¦-intercept is zero, that point at the
origin. This tells us that π itself is
zero for our straight line. And so, our equation simplifies to
π¦ equals twenty seventeenths π₯. This is the equation of the
straight line passing through these two points.