 We're going to talk about finding the equations of lines today. So we already have the equation y equal mx plus b where m is the slope and b is the y-intercept. So we are going to look at a very simple equation first. We want to write the equation of line that satisfies negative 4 of slope in containing 0, 2, and it says, what is the special point, special about 0, 2? 0, 2 is the y-intercept. So that tells us that b is equal to 2. We know that already. And we know what the slope is. As long as we know the slope and we know the y-intercept, we can write the equation of the line, which is exactly what we did here, y is equal to negative 4x plus b, which is 2. So let's try again. Slope is positive 3 halves. It contains a point 0 negative 3. This is the y-intercept. So we just have to say 3 halves times x minus 3 because it's a negative 3b. All right. This time it's a little bit harder. We don't have the y-intercept. This is not the y-intercept. So we have to use a plug and chug. So now we know m, 1 is our x, y is our negative 5. So if we plug back in for y equal mx plus b, everything we know, y is negative 5, equal to m, which is 2, times x, which is 1, plus b, which we're trying to find. So negative 5 is equal to 2 plus b. And if I subtract 2 from both sides, then b is negative 7. So now I know b and I know m. And I can put both of those together to make the equation 2x minus 7. What happens if I don't know slope? Well, I might have to find the slope. So if I have this problem here, 6, 5, and 2, negative 7, I need to find the slope. So we're going to do our slope formula. Negative 7 minus 5, y2 minus y1, over 2 minus 6, x2 minus x1. This is negative 12 on top. 2 minus 6 would be negative 4. So negative 12 divided by negative 4 would be positive 3. I know that slope is 3. I'm going to use the point 6, 5. So x is 6, y is 5, and b is what I don't know. So we plug in chug. So y is 5, equal m, which is 3, times x, which is 6, plus b. Y equal mx plus b. So 5 is equal to 18 plus b. And if we subtract 18 from both sides, we should get a negative 13. And that would give us y equal slope, which is 3, times x, plus b, which in this case is negative 13. If I choose the other point, I would have y is equal to negative 7, equal m, 3, times x, which is 2, remember this is my x, this is my y, plus b. So negative 7 is equal to 6 plus b. And if I subtract 6, I get negative 13. So I have y equal slope of 3 times x, plus my b, which is negative 13. Same equation. So does it matter which point we choose? No.