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3 years ago

What is the slope of the line that is graphed below ?

Mathematics

1 answer:

9966 [12]3 years ago

8 0

The graphed line is y = 1/3x + 2

In order to solve for this, we need to start by finding the slope. To find the slope, we start by selecting two points on the graph. We'll use (0, 2) and (6, 4).

m(slope) = (y2 - y1)/(x2 - x1)

m = (4 - 2)/(6 - 0)

m = 2/6

m = 1/3

Now that we have this, we can use a point and slope intercept form to find the intercept.

y = mx + b

4 = (1/3)(6) + b

4 = 2 + b

2 = b

And we can use the slope and intercept to model the equation as y = 1/3x + 2

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Option C:

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$$=\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}+\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1}+\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}+\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}$

$$+\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}+\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}$

Let us solve the term one by one.

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$$\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}= 80 x^{3} y^{2}$

$$\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}= 40 x^{2} y^{3}$

$$\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}= 10 x y^{4}$

$$\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}=y^{5}$

Substitute these into the above expansion.

$(2x+y)^5=32 x^{5}+80 x^{4} y+80 x^{3} y^{2}+40 x^{2} y^{3}+10 x y^{4}+y^{5}$

The coefficient of $x^{2} y^{3}$ is 40.

Option C is the correct answer.

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