On Week 13 of math 10, my class continued on the Relations and Functions unit. That week, we went more in depth in learning about domain/range, set/interval notation, functions, and function notation. In this week’s blog post, I am going to show you how to determine the x and y intercepts of an equation. Before we begin, we first need to learn some key terms. A Domain is a set of numbers for the independent variable; D={3⊆x⊆5}. A Range is the opposite, being a set of numbers for the dependent variable; R={4⊆x⊆7}. Next, an x intercept is when a set of coordinates is plotted somewhere in the x axis and because of that, it will be at zero for the y coordinate. The y intercept, unsurprisingly is the opposite where the set of coordinates is plotted somewhere on the y axis and is at zero for the x coordinate. Now that we know some key terms that can help us in these examples, we may begin.
For our first example, we have the equation y = 15 – 6x. For this question, we need to find the x intercept, the y intercept, and answer in ordered pairs. So to start off, I like to find the x intercept first because naturally x come before y in the alphabet. So to find the intercepts, we answer the equation similar to how we would using BEDMAS. To begin, we start off by changing the term with the y variable into zero because the x intercept has zero for the y axis. Next we are trying to isolate the x variable so we do the reverse opperation for positive 15 so we subtract 15 from itself and from the zero on the other side. After that we end up with -15 = -6x so to finish we need to divide -6 from both sides and we end up with x = 2.5. Our final answer in ordered pairs is (2.5, 0). Next we are going to find the y intercept. To begin we change the term with x into zero to end up with y = 15 – 0. Because of that, we already end up with our answer in y = 15. Our final answer in ordered pairs is (0, 15).
For our second example, we have the equation 4x – 2y + 16 = 0. We are once again going to begin by finding the x intercept so we change the term with the y variable and get 4x – 0 +16 = 0. Next we are going to isolate x by doing the opposite operation to cancel 16 out so we are subtracting 16 from both sides to end up with 4x = -16. Lastly, we divide both sides by 4 and we end up with x = -4. Our final answer in ordered pairs is (-4, 0). Now for the y intercept, we are once again going to cancel our the term with the x variable and get 0 – 2y + 16 = 0. Next we are again going to isolate the variable and subtract 16 from both sides to get -2 = -16. Lastly we divide both sides by -2 and we end up with y = 8. Our final answer in ordered pairs is (0, 8).