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3 years ago

Straight line graphs: find the equation of the lines shown

Mathematics

1 answer:

nika2105 [10]3 years ago

7 0

Answer:

1. y = -2n + 9

2. y = (1/2)x + 1/2

Step-by-step explanation:

The equation of a line is denoted by y = mx + b, where m is the slope and b is the y-intercept.

Slope is calculated by taking two coordinates and dividing the difference of the y-coordinates by the difference of the x-coordinates. The y-intercept is where the line intersects the y-axis.

Let's choose any two points on the line: (4, 1) and (3, 3). Then:

slope = m = (3 - 1) / (3 - 4) = 2 / (-1) = -2

Now, we can also see that at the point (0, 9), the line intersects the y-axis, so that means b = 9.

The equation is thus y = -2n + 9.

Let's again choose any two points to find the slope: (1, 1) and (3, 2). Then:

slope = m = (2 - 1) / (3 - 1) = 1/2

We can see that the line crosses the y-axis at the point (0, 1/2), so that means b = 1/2.

The equation is thus y = (1/2)x + 1/2.

~ an aesthetics lover

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For this case we have that by definition it is fulfilled:

$a ^ b$

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a: It is the base

b: It is the exponent

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Answer:

-6: It is the base

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2 years ago

How many ways can eight letters be arranged into groups of five where order matters and the first two letters are already chosen

fenix001 [56]

Answer:

120

Step-by-step explanation:

Since we're dealing with a problem where the order matters and the first two letters are already chosen we need to subtract the number of letters and the number of available slots per group.

We use the permutation formula to find the answer, but before that let's check values.

n = 8

k = 5

Now since there are two letters already chosen we have to deduct two from both the value of n and k.

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k = 3

Now we can use the permutation formula:

$_{n}P_{k}=\dfrac{n!}{(n-k)!}$