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# Slope-intercept equation from slope & point (old)

## Video transcript

A line has a slope of 7 and goes through the point negative 4, negative 11. What is the equation of this line in slope-intercept form? So the equation of any line in slope-intercept form is y is equal to mx plus b, where m is the slope and b is the y-intercept. Now, in this problem right here, they tell us the slope. They tell us that a line has a slope of 7. So we know right from the get go that m is equal to 7. So we know the equation of this line in slope-intercept form is going to look like y is equal to, we know m is 7, so 7x plus-- let me make that x a little bit neater-- 7x plus b. And now what we need to do, we need to figure out b, and they give us one more piece of information. They say that the line goes through the point negative 4 comma negative 11. So that tells us that when x is equal to negative 4, then y is equal to negative 11. So we can use this information in what we have or the part of our equation that we've been able to figure out so far. We know that when x is equal to negative 4, y is going to be equal to negative 11. So what b do we need to make that happen? Let's try it out. So y is negative 11 when x is equal to negative 4. So negative 11 is equal to 7 times x-- and in this case x is negative 4-- plus b. And now we can just solve for b. A b that makes this equation, or that satisfies the constraint that when x is equal to negative 4, y is equal to negative 11. So let's see, we get negative 11 is equal to 7 times negative 4 is negative 28 plus b, and now we can add a 28 to both sides of this equation. So let's add a 28. I'm just trying to isolate the b on the right-hand side. And so on the left-hand side, negative 11 plus 28, that is just positive 17. These guys cancel out on purpose. And I just have a b on the right-hand side. So I get b is equal to 17. Let me write it in green. That's not green. We get b is equal to 17. So we know m is 7, they told us that right at the beginning. And now we know b is 17. So the equation of our line is y is equal to 7x, that's our slope. 7 times x plus b, and b here is 17. And if we wanted to graph it, it would look something like this. I'll just do a real rough graph. So if we wanted to graph this line, that's my x-axis, and this is my y-axis. The y-intercept is 17. So that means that the point 0, 17 is on this line. So this point right over here is going to be 0, 17. And our slope is 7. So that means if we move to the right one, we move up t seven. So it's a high slope. So if we move to the right one, we move up seven. Or if we move back one, will move down seven. So we'll move down seven, so the line will look roughly like this. Obviously, haven't done it very exactly, but our line is going to look like. That's going to be a pretty steep upward-sloping line. It has a very high slope, slope of seven. If you move one in the x direction, you have to move up seven. And its y-intercept is at y is 17. When x is 0, y is 17.