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CCSS.Math: , , , , ,

we have the equation negative 5x plus 4y is equal to 20 and we're told to find the intercepts of this equation so we have to find the intercepts intercepts and then use the intercepts to graph to graph this line on the coordinate plane so then graph graph the line so whenever someone talks about intercepts they're talking about where you're intersecting the x and the y axes so let me label my axes here so this is the x axis and that is the y axis there and when I intersect the x axis what's going on what is my Y value when I'm at the x axis well my Y value is 0 I'm not above or below the x axis so the X X let me write this down the x intercept the x intercept the x intercept is when y is equal to 0 right and then by that same argument what's the y-intercept y-intercept what is the y intercept well if I'm somewhere along the y axis what's my x value well I'm not to the right or the left so my x value has to be 0 so the y intercept occurs when X is equal to 0 so to figure out the intercepts let's set y equal to 0 in this equation and solve for X and then let's set X is equal to 0 and then solve for y so when y is equal to 0 what does this equation become I'll do it in orange you get negative 5x plus 4y well we're saying Y is 0 so 4 times 0 is equal to 20 4 times 0 is just 0 so we can just not write that so let me just rewrite it so we have negative 5x is equal to 20 we can divide both sides of this equation by negative 5 by negative 5 the negative 5s cancel out that was the whole point behind dividing by negative 5 and we get X is equal to 20 divided by negative 5 is negative 4 so when y is equal to 0 so when y is equal to 0 we saw that right there X is equal to negative 4 or if we wanted to plot that point we always put the x-coordinate for it first so that would be the point negative 4 comma 0 so let me graph that so if we go 1 2 3 4 that's negative 4 and then the y-value is just 0 so that the point is right over there that is the x-intercept y is 0 X is negative 4 notice we're intersecting the x-axis now let's do the exact same thing for the y-intercept let's set X equal to 0 so if we set X is equal to 0 we have negative 5 times 0 plus 4 y is equal to 20 well anything times 0 is 0 so you can just put that out of the way and this remember this was setting X is equal to 0 we're doing the y-intercept now so this just simplifies to 4 y is equal to 20 we can divide both sides of this equation by 4 to get rid of this 4 right there and you get Y is equal to 20 over 4 which is 5 so when X is equal to 0 Y is equal to 5 so the point 0 5 is on the graph for the for this line so 0 5 0 x is 0 and Y is 1 2 3 4 5 right over there and notice when X is 0 we're right on the y-axis this is our y-intercept right over there and if we graph the line all you need is two points to graph any line so we just have to connect the dots and that is our line so let me connect the dots try my best to draw as straight of a line as I can well that I can do a better job than that to draw as straight of a line as I can and that's the that's the the graph of this equation using the x intercept and the y intercept