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a line has a slope of seven 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 7 X 7 X plus let me make that X a little bit neater 7 X plus 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 would be 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 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 plus plus B and now we can just solve for B a B that 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 28 to both sides of this equation so let's add 28 I'm just trying to isolate the B on the right hand 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 we get that's not green we get B B is equal to 17 so we now 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 then this is my y-axis y axis the y intercept is 17 so that means at the point 0 17 is on 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 7 so it's a high so if we move to the right 1 we move up 7 or if we move back one will move down 7 so we'll move down 7 so the line will look roughly like this I 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 7 if you move one in the x direction you have to move up 7 and its y-intercept is at Y is 17 when x is 0 Y is 17