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Use the 2! 3x process 6x2 2 the slopethe graphthe function the L polnt:...

Question

Use the 2! 3x process 6x2 2 the slopethe graphthe function the L polnt:

Use the 2! 3x process 6x2 2 the slope the graph the function the L polnt:



Answers

Find the slope of the graph of $y=f(x)$ at the designated point. $$f(x)=3 x^{2}-2 x+1,(1,2)$$

So my goal in this example is to find my soap and mo intercept. Until then, use those pieces of information to grasp the line. Slope is represented by the variable M Y. Intercept is represented by the variable B, and so that means I'm talking about the equation. Y equals MX Plus now in this equation, trying to identify soap in my intercept my slope it is 2/3. It's always my coefficient of X, and my Y intercept is always that number that's being added or subtracted on the end, which in this case, is too. Now these two pieces of information why intercept is actually a point on the line slope is how sleep the line is. But why intercept tells you where to start. That means my line that I don't even see it is going across the Y axis at two right here, so I can put a point there. Now I can use my slope to get to all the other points on my line. It's like a road map and slope Israeli a changing. Why, over change in X or vertical changed the horizontal change. And since my self is already a fraction I can actually just match these things up right away. So what this says is that for every two spaces, I go up on my line changed why I go three spaces to the right. So from here I could go 12 123 and then I could put a point in that spot. I could stop right now and just connect. Or I could just block multiple points to continue along this pattern. I personally like doing this. I think it makes it a little bit easier to connect. I also think when you get to systems of equations, it'll make it a little bit simpler, hopefully to find a point of intersection, especially if it's an integer. So then you would connect with preferably something straight, like a straight edge or the edge of a notebook. And so that's what our lives would look like.

Yeah. Hello, here we see. The graph of Y is equal to negative three have X plus six. Um Here, graft in death most so the slope of this uh this line is just gonna be the coefficient on our X. So the slope is going to be negative three hands.

Okay, so we want to find our slope. I'm here. So let's recall that that's the difference of our Y values or f of to minus F A negative to over our X values. So here we can replace this with six minus a negative one. So that's a plus one over two minus and maker Tuesday That's close to, so we're going to get a 7/4 for a slope.

In this problem. We're graphing the line with the equation y equals negative six X. Now, if you think about slope intercept form Y equals MX plus B. The bee is the Y intercept. The M is the slope. So for our equation, we don't have a y intercept showing. We can just pretend there's a plus zero on their and our Y intercept. Zero. So that's the point with coordinates 00 and our slope is negative. Six and negative. Six can be written as negative six over one. So you see a rise over a run. Okay, so the first thing we want to do is plot. Are y intercept a 00? We should also establish a scale. So I'm just gonna go by one's on each axis and then from our Y intercept, we want to go up six and over one and make sure we're going over in the direction that gives us a negative slope. So from our white intercept up six and over one gives us another point there. We could do it again. Up six and over one. We could also go from our Why intercept down six and over one just making sure we go in the proper direction to get a negative slope, and then we're gonna attempt to make our line nice and straight. Your line is hopefully a little straighter than mine. Maybe you can use a ruler on that, and there's our line.


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