### Video Transcript

Determine the equation of the line passing through ๐ด: zero, 16 and ๐ต: one, negative nine in slope-intercept form.

So in this question, weโre given the coordinates of two points that lie on a straight line, and weโre asked to determine its equation. Weโve also been asked for the equation in a specific form, slope-intercept form. This is ๐ฆ equals ๐๐ฅ plus ๐, where ๐ represents the slope of the line and ๐ represents the ๐ฆ-intercept. In order to answer this question, we need to determine both of these values, the slope and the ๐ฆ-intercept.

So letโs look carefully at the information in the question and the coordinates of the two points weโve been given that lie on the line. The first of these two points, ๐ด, has coordinates zero, 16. As the ๐ฅ-coordinate of this point is zero, this is a point on the ๐ฆ-axis. And therefore, these are the coordinates of the ๐ฆ-intercept. The ๐ฆ-coordinate is 16 and this tells us the value of ๐ in our equation is also 16. So we can substitute this value of ๐ into the equation of our line. So we have that ๐ฆ equals ๐๐ฅ plus 16 for a value of ๐ that we now need to calculate.

Remember, ๐ represents the slope of the line. If we know the coordinates of two points on the line โ which weโll refer to as ๐ฅ one, ๐ฆ one and ๐ฅ two, ๐ฆ two โ then the slope can be calculated using this formula: ๐ is equal to ๐ฆ two minus ๐ฆ one over ๐ฅ two minus ๐ฅ one. It doesnโt matter which of the two points we think of as ๐ฅ one, ๐ฆ one and which we think of as ๐ฅ two, ๐ฆ two. Iโm going to choose to subtract the coordinates of point ๐ด from those of point ๐ต.

So letโs calculate the slope of this line. ๐ is equal to ๐ฆ two minus ๐ฆ one, so that is negative nine minus 16. And then I need to divide by ๐ฅ two minus ๐ฅ one, so thatโs one minus zero. My calculation for the slope simplifies to negative 25 over one, and of course thatโs just equal to negative 25. The final step in answering this question is I need to substitute this calculated value of ๐ into the equation of the line.

So in doing so, I have that ๐ฆ is equal to negative 25๐ฅ plus 16. And thatโs our answer to this problem, the equation of the line in slope-intercept form.