Find the slope 𝑚 and the
𝑦-intercept 𝑏 of this straight line.
First, let’s note what the slope
is. Sometimes we say that the slope is
the rise over the run, which is to say it’s the changes in 𝑦, the vertical changes,
over the changes in 𝑥, the horizontal changes. And the 𝑦-intercept 𝑏 is the
point where the line crosses the 𝑦-axis.
Using this diagram, we should be
able to identify both the slope 𝑚 and the 𝑦-intercept 𝑏. We can calculate the slope, the
changes in 𝑦 over the changes in 𝑥, between any two of the points on the line. For example, we could start at the
point one, zero. And we could go to the point three,
two. The rise, the changes in 𝑦, is
positive two from zero along the 𝑦-axis to two along the 𝑦-axis. And the run, the changes in 𝑥 or
the horizontal changes, are also positive two, from one to three along the
Our changes in 𝑦 were positive
two, and our changes in 𝑥 were positive two. Two over two is one, which tells us
that our slope is one. We could confirm this. If we start at the point zero,
negative one, we go up one and right one to get to the point one, zero. And one over one is again one.
Now, we want to consider the
𝑦-intercept, the place where this line crosses the 𝑦-axis. The 𝑦-axis is the vertical
line. And this line crosses the 𝑦-axis
here, at zero, negative one. The 𝑏-value will be the place
along the 𝑦-axis this point crosses. And that is negative one.
You’ll probably remember that the
general form for a linear equation is 𝑦 equals 𝑚𝑥 plus 𝑏. Using this information, we could
write an equation for this line, which would be positive one times 𝑥 minus one. But one times 𝑥 is just 𝑥. So, the equation for this line
would be 𝑦 equals 𝑥 minus one. And under these conditions, the
𝑚-value is one and the 𝑏-value is negative one.