 This video is going to talk more about slope and interpreting slope. So slope is the rate of change. It is the change in y per the change in x. And if you just kind of keep that in mind, the change in y per the change in x, that's really the way that you interpret it. If you think about the rate of your car traveling down a road, it is miles per hour. That's the rate. When we want to interpret y intercept, remember that is the point 0B, where x is 0 and if we're interpreting it would be 0, whatever its units are. And then y would be B units. So if you interpret it, you're saying that x's value is 0. So if it's in years, you're talking about the 0 year. So this is often you would say that when time began, because that's a lot of times what our x is. So let's look at this problem. Interinterpret the slope and the y intercept and use them to make a table of three ordered pairs. The median annual income of women with a bachelor's degree is given by this equation. And then we have the equation and then it tells us that x is the number of years after 1990. So that's our x. And then if we could just define our y, then it will be interpreting pretty easy. And the y is usually what they talk about the problem being. And so that would be the median annual income. So we'll just call that income. So now let's go and interpret our slope. Remember, slope is the change in y over the change in x. So that means it's going to be the change in income over the change in years. Our number happens to be 1,100. It means that it's at $1,100 and it's increasing because it's positive. So it's at $1,100 increase in y. And y is income per the x and x is in years. Now they ask us also to talk about the y intercept. Where the y intercept is 0b. And remember, when you have it in y equal mx plus b form, it's just this constant. So it's 27,645. Well, this is our x. So that means years. Our y. So that means dollars. So it means that in year zero, which is 1990. So we say in 1990, when time began, the median annual income was our y intercept. Or we could say annual income was $27,645. So let's look at this problem and again interpret what we know. So it says the car's value is given by y is equal to negative 2,500 x plus 15,000. Well, this is our m and this is our b. And we need to know what x and y are as well. Then we can really go to town on trying to interpret these. Well, x is the age of the car. So it's going to be in years. Its unit is years. And the car's value is what we're talking about. So the value in dollars. So again, slope is equal to negative 2,500. And it's, if we think about it as being negative 2,500 over 1, which is our y, which is dollars. And our x, which is years. So we just have to remember this part too and then we can interpret. So value, and it's a negative this time. We say it decreases because it's a negative. And it decreases by that amount, $2,500. Remember it's in dollars. Per. And then it happens every year. So per year. If we look at the y intercept, it's the zero. And again, it's our constant. Our b here we said was 15,000. This is year zero. And this is the value of the car. And the car was new. That would be the beginning. The car was new. The value was 15,000. Interpreting this one, the daily cost to rent a car is given by this equation, where x is the number of miles driven. And again, let's talk about what our y and our b and our mr. So this is slope. And it's a positive slope. And this is our b. And positive slope means that we're going to increase, just so we can get our interpretation in there. O is .50 over one. This is my y. This is my x. So when I interpret here, I'm going to say .50 cost, which is going to be in dollars. And one is going to be miles because the x's are in miles. So interpreting then, we say that the cost, that's the y. And then we said it's going to increase because it was a positive slope. So we either say increase here or we say decrease. And then we say per, and then it's the x. And in this case, it would be miles. So this would be our interpretation formula sense. If we talk about y intercept, it's zero. And we found the b over here to be 40. Beginning in the beginning, the y was, and then you give whatever it is. So when we talk about beginning here, it would be zero. This is miles. Driving zero miles, that's the beginning. The cost, that's the y, to rent is, and what is it? This is our b again. And it's in dollars. So it would be $40. All right. So if we want to look at some problems that are real life situations, and we have to find that slope, let's look here. It says the pitch of the roof that rises six inches for each 12 inch, it extends horizontally. So remember, if we want to talk about slope, the y's are the vertical, that's up and down, over the horizontal. That's the left and right. So now we really just kind of have to fill it in. What's the vertical? It rises, that would be the vertical, so six inches per the 12 inches horizontally. And then we would just want to reduce it. And we know it's going to be inches, but it's going to be one half, one inch vertically per every two inch horizontally. Reading this problem, if the door is 15 inches above the ground, how long will the wheelchair ramp be for a slope to be 112? We need to think about this. I'm very visual, so I'm going to draw my door here. And that's above the ground. So here's the ground up here, and here's my door. So this is 15 inches, two lines means an inch. And then I know that I want to draw or have some kind of ramp from that ground to my door. So we know this is 15, and actually it starts here. So our rise is 15. Well, I know that this ramp is going to be 112, but I don't know what my run is. In fact, let's give that a different number. I don't know what the run is. So let's put in what we know then. M is equal to rise, which I know is 15, over the run, but I don't know what that is. And it is also equal to 112. So this is really the equation that I'm working with. Well, I have a fraction. So to solve that, I need to multiply both sides of the equation by x. These x's will cancel leaving me with 15. And when I multiply 112 by x, I just get 112x. And if we divide by 112 and divide by 112, then we have 15 divided by 112. And we get 0.13 inches.