Find the slope of the following line. 0.5 x + 0.2 y = 3 0.5x+0.2y=3

this problem, we are asked to find the slope of the following lines, and here we have this equation. Now notice in this problem we are not given a graph, so we're going to have to use the equation for the slope, which is going to be y two minuteus y one, or the rise, divided by x two minus x one, or the run. So let's see how we can find the slope. Now, I'm gonna need two points to go off of, and I'm gonna find those points using the equation we have. The two points I'm going to use are gonna be the x intercept, and I'll also use the y intercept. Now the way I can find the x intercept is by setting y equal to zero, and the way you can find the y intercept is by setting x equal to zero. So let's start with finding the y intercept. Well, I'm gonna go to this equation, and I'll set y equal to zero. So we're going to have 0.5 x plus 0.2 times zero, because we're replacing y with zero, and that's all going to equal three. Now, this 0.2 times zero is just going to give us zero, leaving us with point five x plus zero equals three. Now 0.5 x plus zero is just 0.5 x, and I can go ahead and divide both sides of this equation by 0.5. And that'll get the 0.5 to cancel, leaving me with just x. And what is three divided by 0.5? Well, 0.5 is a half, and if you divide a half into three, you end up getting six. Right? You can check that on a calculator too, or just recognize this would be one half in the denominator and then flip it and bring it to the top. Either way, you will get six as your result. So we get an x value of six or y value zero, so our x intercept is gonna be the point six zero. Now let's go ahead and check on the y intercept. For the y intercept, we need to set x equal to zero, so we'll get 0.5 times zero, replacing that x with zero, and we're gonna get plus 0.2 y is equal to three. Now, of course, this 0.5 times zero all just goes to zero, leaving us with zero plus 0.2 y is equal to three. Now from here, we're just gonna have 0.2 y. That's good because the zero doesn't do anything, so we'll have zero plus 0.2 y, which is 0.2 y equals three. Then I can just divide 0.2 on both sides of this equation. And this gives 0.2 to cancel here. And what exactly is three over 0.2? Well, again, you can check this on a calculator because this will give you y by itself, and you should get 15. So we get a y value of 15 when we go ahead and solve for y. So notice that we now solved for y, and we already know that our x is zero, so we get the point 15. So we now have our x intercepts and our y intercepts, and we can go ahead and use these as point 1.2. So let's go ahead and use our slope formula. So we have y two right here. I went ahead and said this was point two. It doesn't matter what you pick as point two or point one as long as you're consistent. But since we see this as point two, I'm gonna have 15 minus, and then we have y one, which is gonna be this y value in point one. I can see that that's zero. And I'm gonna divide that by x two minus x one, where this x two is going to be my x right there for point two, which is zero. Then we'll have minus x one, which I can see is six. So we end up getting 15 minus zero over zero minus six. Now from here, I can go ahead and solve what we have. So 15 minus zero is 15 minus six is negative six. Now five is the same thing or 15 is the same thing as three times five, and six is the same thing as two or as negative two times three. I can go ahead and cancel those threes, which will give me a slope of negative five half. So this right here is going to be my slope, and that will be the solution to this problem. So that is how you can find the slope of this line based on the two points, the x and y intercepts, which we also found. Hope you found this video helpful, and let me know if you have any questions.