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CCSS.Math:

we have three lines and we have to figure out which of the three are parallel so line a and it can't be parallel on its own has to be parallel to another of the three lines so the equation for line a is y is equal to 3/4 X minus for line B line B is 4 y 4 y minus 20 is equal to negative 3 X and then line C line C is negative 3x plus 4 y is equal to 40 so to figure out if any of these lines are parallel to any of the other lines we just have to compare their slopes if any of these two lines if any two of these lines have the same slope and there are different lines they have different y-intercepts then they're going to be parallel now line a it's very easy to figure out its slope it's already in slope intercept form this is M X plus B the slope is 3/4 and the y-intercept which isn't as relevant when you're figuring out parallel lines is negative 4 so let's see what the other character slopes are this isn't in any kind of standard form it's not in standard form slope intercept or point-slope form but let's see what the slope of this line is so to get it into slope intercept form which is really the easiest one to figure pick out the slope from let's add 20 to both sides of this equation so let's add 20 to both sides the left-hand side those cancel out that was the whole point you get for Y is equal to negative 3x plus 20 and now we can divide everything by 4 divide everything by 4 just dividing both sides of this equation by 4 we are left with Y is equal to negative 3/4 X plus 5 so in this case y-intercept is 5 but most importantly the slope is negative 3/4 so it's different than this guy this is negative 3/4 this is positive 3/4 so these two guys definitely aren't parallel let's move on to this guy this guy written in standard form let's get the X term on the other side so let's add 3x to both sides of this equation let's add 3x to both sides of this equation left-hand side these cancel out we're just left with 4y is equal to 3x plus 40 or 40 plus 3x either way now we can divide both sides by 4 we have to divide every term by for the left-hand side you're left with Y the right-hand side you have three fourths X plus 10 so here our slope is 3/4 and our y-intercept if we won't care about it is 10 so this line and this line have the exact same slope 3/4 and there are different lines because their y-intercept is different so we know that a and C are parallel lines and B is not parallel to neither one of the other two