### Video Transcript

What is the ๐ฆ-intercept of the line passing through negative two, negative 16 and one, negative four.

Weโve been given two points that lie along the same line. And weโre trying to find the ๐ฆ-intercept of this line. If the line is given in the form ๐ฆ equals ๐๐ฅ plus ๐, the constant value ๐ represents the ๐ฆ-intercept.

In order to take these two points and write an equation for this line, weโll first need to calculate the slope. If weโre given two points, we can find the slope by taking the ๐ฆ-coordinate of the second point, subtracting the ๐ฆ-coordinate of the first point, and writing that as a fraction over the ๐ฅ-coordinate of the second point minus the ๐ฅ-coordinate of the first point. More commonly, we just say ๐ฆ two minus ๐ฆ one over ๐ฅ two minus ๐ฅ one. It doesnโt matter which point we label as point one and which point we label as point two as long as weโre consistent.

So we have negative four minus negative 16 in the numerator and one minus negative two in the denominator. Negative four minus negative 16 is negative four plus 16, which is 12. And one minus negative two is one plus two, which is three. The slope of this line is four. We can take this slope and one of these points and use it to help us solve for the ๐ฆ-intercept.

If ๐ฆ equals ๐๐ฅ plus ๐ and our slope is four and we have the point one negative, four. We can plug in one for the ๐ฅ-value and negative four for the ๐ฆ-value. Four times one is four. And so we can say that negative four equals four plus ๐. To find what ๐ is, we subtract four from both sides of the equation. Negative four minus four is negative eight. And four minus four is zero. Our ๐-value is then equal to negative eight. Our equation of this line must be ๐ฆ equals four ๐ฅ minus eight. And weโre only looking for the ๐ฆ-intercept, which is negative eight.

We solved this problem finding the slope and then the ๐ฆ-intercept form of the line. We could also try and solve by graphing. Once you sketch a graph, weโll add a point at negative two, negative 16 and one, negative four and then connect those points. We can see that this line crosses the ๐ฆ-axis at negative eight, which confirms the ๐ฆ-intercept of negative eight. Now, the key here to solve by graphing is that you need to be accurate with your lines and spaces. You would likely want to draw this on graph paper to make sure you were getting accurate points. Otherwise, you can solve using the slope-intercept form.