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CCSS.Math: , ,

a line has a slope of negative three-fourths and goes to the point 0 comma 8 what is the equation of this line in slope-intercept form slope-intercept form so any line can be represented in slope-intercept form is y is equal to MX plus B where this M right over here that is the slope of the line and this B over here this is the y-intercept y-intercept of the line let me draw a quick line here just so that we can visualize that a little bit so that is my y-axis and then that is my x-axis my x-axis so let me draw a line and since our line here has a negative slope I'll draw a downward sloping line so let's say our line looks something like that let's say it looks something like that so hopefully we're a little familiar with the slope already the slope essentially tells us look start at some point on the line and go to some other point of the line measure how much you have to move in the X direction that is your run and then measure how much you have to move in the Y direction that is your rise and our slope is equal to rise over run and you can see over here it would be downward sloping because if you move in the positive x direction we have to go down our run if I run is positive our rise here is negative so this would be a negative over positive give you a negative number and that makes sense because we're downward sloping the more we go down in this situation for every step we move to the right the more downward sloping will be the more of a negative slope we'll have that's slope so that's slope right over here the y-intercept just tells us where we intercept the y axis so the y intercept this point right over here this is where the line intersects intersects with the y axis this will be the point 0 comma B and this actually just falls straight out of this equation when X is equal to 0 so let's evaluate this equation when X is equal to 0 y will be equal to M times 0 plus B anything times zero is zero so Y is equal to zero plus B or Y will be equal to B when X is equal to zero when X is equal to zero when when X is equal to zero so this is the point zero comma B now they tell us what the slope of this line is they tell us a line has a slope of negative three-fourths so we know that our slope is negative three-fourths and they tell us that the line goes through the point zero comma eight they tell us we go through that let me just in a new color I've already used orange let me use this green color they tell us that we go through the point zero comma eight notice X is zero so we're on the y-axis when X is zero we're on the y-axis so this is our y-intercept so B we could say we could do a couples our y-intercept is the point 0 comma 8 or we could say that B remember it's also 0 comma B we could say B is equal to 8 so we know M is equal to negative 3/4 B is equal to 8 so we can write the equation of this line in slope intercept form it's y is equal to negative three-fourths negative three-fourths times X times X plus B plus 8 plus 8 and we are done we are done