Find the slope & y−intercepty-intercepty−intercept of the line given by the equation 3x+2y−6=03x+2y-6=03x+2y−6=0

m=−32,b=3m=-\frac32,b=3m=−23,b=3

Find the slope & y − i n t e r c e p t y-intercept y − in t erce pt of the line given by the equation 3 x + 2 y − 6 = 0 3x+2y-6=0 3 x + 2 y − 6 = 0

Hey, everyone. So let's take a look at this practice problem. So I'm given this equation of this line, 3x+2yminus6 is 0, and I wanna find the slope and the y intercept. So remember those two variables are m and b. Slope is m, y intercept is b. And notice how in this equation, I'm not given something that looks like y, slope intercept form, y equals an x plus b, or the point slope form. I'm given an equation that kind of look in standard form where, remember, all the terms are on the left side, and then it just equals 0 on the right side. So I can't just sort of extract m and b directly from this equation. I'm gonna have to first rewrite this equation so that it looks like y equals mx plus b. And, basically, what you have to do is you have to solve for y. So let's go ahead and do that. So I've got 3x+2yminus6 is 0. I'm just rewriting this. Now I wanna start isolating y on the left side. So first thing I have to do is I'm gonna move the 6 over to the right side, and I have to add 6 to both sides. Then I take the 3 x, and I also have to move it to the right side. And in that case, I have to subtract 3 x over here. So, basically, what ends up happening is you're gonna get 2 y on the left side that stays, and then you get, negative 3x+6. Alright? Now we're not quite done yet because this doesn't yet look like y equals mx plus b. I still have a coefficient in front of the y, so I have to get rid of that now. So the second step is I have to divide everything in this equation by 2. Whatever you do to one side, you have to do to the other, and so I end up with just y on the left side, which is good, and this ends up being negative 3 halves x, and then 6 over 2 actually just ends up becoming 3. So notice how if we look at this equation here, now I have solved for y, and it looks like I have a coefficient in front of x and then some constant term at the end. So this does look like y equals mx plus b. So now that we have rewritten this equation in, slope intercept form, we can very clearly see what the m and b are. So in this case, my m is equal to the negative 3 halves, so that's my slope, and my y intercept, on the other hand, is just equal to, this term over here, which is just positive 3. So these are your two answers. Alright? Slope is negative 3 halves, and the b term is just equal to 3. So that's it for this one, folks. Let me know if you have any questions. Hopefully, that made sense. Thanks for watching.