Hello wonderful mathematics people. This is Anna Cox from Kellogg Community College. Linear functions. Slope of a line is the change of YS over the change of X. Sometimes we use a small triangle called a delta which stands for change. So delta Y over delta X or Y 2 -, y one over X 2 -, X one. This is equivalent to if we had the X1 Y ones coming first. So Y 1 -, y two over X 1 -, X two. A couple types of slopes are positive slope where we start in the lower left and we go through to the upper right, or a negative slope where we start in the upper left and come down into the lower right. We're going to look at two more slopes in just a minute. Forms of a line. We have slope intercept, which is Y equal MX plus B where M is the slope and 0B is the Y intercept. We have point slope which is y -, y one equal M times the quantity X -, X one M is the slope. X1Y1 is any point on the line. Point slope is probably one of the most powerful forms and it comes directly from our slope formula. If you look at your slope formula, you had M equal Y 1 -, y two over X1 minus X2. If you just cross multiply and realize those little ones and little twos just signify that they come from the same point. So this X1 Y 1 is now like our plane X and plane Y, and the X2 Y 2 is like our X1 Y. One general form is AX plus B y = C It's considered the pretty form because AB and C are all integers and the first term is always positive or zero. Horizontal lines. If we draw on any horizontal line and give ourselves two points, we're going to find the slope. So on this horizontal line, this first point would be 1, 2 and the second point would be 4, 2. Using our slope formula, it's the change of YS over the change of X's. So we get 0 / 3 which is just zero. So horizontal lines have zero slope and they're of the form Y equals some number Y equal B because B is the Y intercept. So the slope IS0Y intercept 0B. We're going to look at vertical lines next. Given any vertical line, give yourself two points, in this case 21 and 12324 doing the changes or the slope formula again the change of YS over the change of X. This time we get 3 / 0, but we know we can't divide by zero, so it's an undefined slope and a vertical line is of the form X equal A and there is no Y intercept. Thank you and have a wonderful day. Thank you and have a wonderful day.