Graph the equation 9 x + 6 y + 18 = 0 9x+6y+18=0 9 x + 6 y + 18 = 0 by finding the intercepts .

Hey, everyone. So in this practice problem, we're supposed to graph this equation 9x plus 6y plus 18 equals 0, not by first rewriting it in slope intercept form or something like that. We actually just have to find the intercepts. Notice how this is an equation in standard form. We have everything on the left side, a equals 0 on the right side, and we have something that looks like a x plus b y plus c equals 0. So how do we find the intercepts? Basically, we're just gonna set the x values and the y values equal to 0 and then solve that equation. So let's go ahead and get started here. In order to find out the x intercepts, remember the x intercept is where the y value equals 0. So you have to set y equal to 0 to find the x intercepts. So rewrite this equation, 9x plus 6y plus 18 equals 0. Now what we do is we're gonna set y equal to 0 and then solve this equation for x. So I'm just gonna replace my y with just 0, and that term just completely goes away. 6 times 0 is just 0 minus or sorry. Plus 18 equals 0, and what you end up getting here on the other, when you move the 18 to the other side and subtract, is you end up getting 9 x equals negative 18. And if you solve for this, you just sort of divide by 9 on each side. You're gonna get x is equal to negative 2. So I've solved this equation here for x, which means that I know that my x intercept of this line is gonna be negative 2. So this graph is gonna cross the x axis at negative 2, but that's not enough to figure out what the graph looks like because it's only one point. So now what I have to do is I also have to do the same exact thing, but I have to do this for the y intercept. Remember, for the y intercept, you're now just gonna set x equal to 0 and then solve. So now we're gonna do is 9 x plus 6 y plus 18 equals 0, and now, basically, you're gonna set the x value equal to 0, and this whole first term will go away. So this equals 6 x, and then basically what happens is this 18 goes to the other side. You subtract 18 from both sides, and you just get 6 y equals negative 18. And now what happens is you're gonna divide 6 from both sides. This goes away, and you get y equals negative 3. So I now have my 2 intercepts. I know that x is equal to negative 2, and my y is equal to negative 3. So now that I have two points over here, this point and I have this point over here, now oh, sorry. I'm sorry. This is gonna be negative 3. Now I can connect these points with a line, and that's gonna be my equation. So, basically, I'm just gonna draw a line that kind of looks like this over here, and that is gonna be the equation of my line. Alright? So that's again how to solve these kinds of problems. We have to find the intercepts, and you can't first convert it into slope intercept form. However, if you did convert to slope intercept form, you would see that it has a y intercept of negative 3. Alright? So that's it for this one, folks. Thanks for watching.