Hello wonderful mathematics people. I'm Anna Cox from Kella Community College. The equation Y equal two X -, 3. We're going to use what's called AT chart and the T chart just means we're going to stick in X values and Y values. If we stick in X values, we're going to usually use a couple positive zero and a couple negative. So when I put 2IN for my XI want to find my Y value Y 2 * 2 - 3 so 4 - 3 would give me AY value of one that's an ordered pair. When X IS2Y is 1, the next one we're going to stick one in for X 2 * 1 - 3, so 2 - 3 is -1. This is a new ordered pair. When X IS1Y is -1, following the same procedure, we're going to stick 0 in for our X and we're going to get AY value of -3 once again, a new .0 negative 3 when Y is -1 when sorry, when X is -1 negative 2 -, 3 is -5 once again another new point, X is -1 Y is -5. And finally, for this example, we're going to stick in -2 for our X and we're going to get -7 out for our Y. Once again, another point. So now we can actually graph these points. If we graph these points, we're going to have two one positive 2/1. So to the right two up one, to the right one down 1, none right or left and down 3, left one down 5, left two down 7. When we connect that line, we have a graph to find intercepts of a graph to find the X intercepts. The intercept is going to be in the form a comma 0. So we're going to set Y equal to 0 and solve for X. For AY intercept 0B, we're going to set X equal to 0 and solve for Y. So if we look in an equation such as Y equal X ^2 - 9, if we wanted to find the X intercepts, we're going to set Y equal to 0. So y = 0, X squared -9 is the difference of squares, so X - 3 * X + 3. So we know that X - 3 = 0 and also X + 3 = 0, X equal 3, X equal -3 so when Y is 0X is 3 and also -3. So if we come over here to our graph, there's 30 here's -3 zero. We want to figure out what our Y intercept is. For our Y intercept, we're going to put zero in for our X so that when 0 is our X -9 comes out for our Y. Now if we want this to be a little more accurate, we can always plot a few more points. Say what happens if we have F of one? Well, we put one in for our X and we get out -8. So this is really a point. This is the point when X IS1Y is -8. Now, because of symmetry and because we're squaring this, we also know that -1 will give us that -8. What happens for F of two? Well, 2 ^2 - 9 four -9 negative 5 it's a 2 -5, so 2 negative 512345. We'd also have -2 negative 5 due to symmetry. So there's your X intercepts and your Y intercepts.