 Hey math learners, Mr. Marks here, your friendly neighborhood math teacher. Remember, it's not just about getting the right answers, it's also about learning and growing along the way. Now today's multiple choice problem comes to us from Pennsylvania's Keystone exam sampler pack and was user requested by at me as a toilet on YouTube. Now this problem involves a little bit of linear equations, so what do you say we uncover the mysteries this problem holds together? First let's read the problem's instructions. The equation 3x plus y equals 8 describes a function of x, which graph represents the function? All right, it looks like we have four graphs to choose from here. There are so many ways that we could proceed, it could be quite overwhelming. What ways are you thinking of for today? What do you say we first start by making some observations? For each of them, let's first note the y-intercept. The y-intercept of a line is the value of y, where the line crosses the y-axis. So for a, our y-intercept is 8. For b, our y-intercept is 0. For c, our y-intercept is 8. And for d, our y-intercept is 8. Hey, what a great start. Next let's make some observations of the line's slopes. Remember that the slope of a line at its plainest is simply a measure of a line's steepness moving left to right. So for a, our slope is negative. Because from left to right, the line appears to be downhill. For b, our slope is positive. Because from left to right, the line appears to be uphill. For c, our slope is positive. And for d, our slope is negative. Fantastic. We have quite the collection of observations at this point. Now it's just time to read the problem's instructions one more time to see how we might use these observations to our advantage. Now we are being asked to find which of these four graphs represents the function 3x plus y equals 8. Currently, this equation is written in standard form. Or ax plus by equals c. But because we have these great slope and y-intercept observations, what do you say we rewrite this equation in slope-intercept form? Or y equals mx plus b, where m is the value of the slope of the line and b is the value of the y-intercept of the line. First, we need to move the quantity with the x variable. So we will subtract 3x from both sides. And with this simple change, we now have our equation written in slope-intercept form. So the y-intercept that we are looking for has a value of 8. And the slope that we are looking for has a value of negative 3. All right, now let's use this information to narrow down our choices. Option A has a y-intercept of 8 and a slope that is negative. So it could still be A. And look, option B has a y-intercept that is 0, which is not equal to 8. So we know it can't be option B. Let's cross that option out. Hey, an option C has a slope that is positive, which could never equal negative 3. So we know it can't be option C as well. And option D has a y-intercept that is 8 and a slope that is negative. So that leaves us with options A or D. Just like that, we've narrowed down our choices. But where do we go from here? How do we decide between option A and option D? Again, there are so many ways that we can proceed. It can be quite overwhelming. What ways are you thinking of? For today, let's determine which of these two remaining options has a slope of negative 3. And for that, we're going to use our handy-dandy slope triangle and the concept of rise over run. First, we'll mark and note two points on option A's line that have easily named coordinates. Mark one point here, not here, not here, oh, and here. Next, draw horizontal and vertical lines from the points to form a right triangle. Count the vertical distance to determine the rise. Here, we go down one, so the rise is negative 1. Count the horizontal distance to determine the run. Here, we go right 3, so the run is 3. Now slope is rise over run, so option A's graph has a slope of negative 1 over 3, which is not equal to negative 3. So we know it can't be option A. But wait, there's more. Though we now know the answer is D. I want you to confirm whether D really is the answer or do we need to rethink our steps. Can you calculate the slope of option D using rise over run and confirm that it's negative 3? Take this as an opportunity to challenge yourself. Additionally, why don't you ponder these questions? What error in thinking would lead somebody to select A? What about B or C? Let me know what you come up with. Hey, props to you for taking some time out of your day to do some math with me. I hope you followed along, and if you made mistakes, that's all good. Just remember that every mistake is a step towards learning something new. This is Mr. Mark, signing off. I'll see you next time with another math problem. What did you think? Did you approach this problem differently? Let me know in the comments. And if you enjoyed this problem, show your support by liking and sharing this video. And don't forget to follow my page to stay up to date on more math related content. Until next time.