Answer:
A. 2
B. 3
Step-by-step explanation:
Remember that the slope of a function is rise over run, or change in y over change in x
The "formula" for this would be [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where you're plugging in the values of the corresponding points (x1, y1) and (x2, y2)
I know all the x's and y's seem confusing but it'll make more sense once we actually apply it
Let's actually start with function b, since there is a graph to help you visualize this. The slope is how many squares up the line travels after going right 1 square. For example, look at the point (1,1) and count how many squares up it goes until the next point (2,4)
Its 3 squares up! and from (1,1) to (2,4) we've moved to the right only one square
so per every 1 square to the right, we move up 3
3/1 = 3, so the slope for b is 3
Note that you can do this with any two points on this graph, so if you started with the same point (1,1) and this time you counted all the way to (4,10), you would find that for 3 squares to the right, you go up 9
but now we need to find how far up you go for ONE square,
so you would do 9/3 = 3
3 up per one square over!
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okay, now let's apply this to function A
for this next step, remember that this works for any two points on the line
you can see that when x is at 1, y is at 5, so that represents a point at (1,5)
there is also a point at (2,7)
now imagine in your head you are looking at line that goes from (1,5) to (2,7)
how far up does the line go? Because you are going from 5 to 7, it goes up 2. If you're working with bigger numbers you can simply subtract, like 7-5 = 2.
next we need to know how far over the line goes. The x values go from 1 to 2, so that means you move one square to the right. This makes sense because 2-1 = 1
so, per every 1 square over, you move up 2, and therefore the slope is 2
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I hope this helps, let me know if you need some clarification :)
