A line passes through (-1,5) and (1,3) what is the equation of the line

Mathematics

1 answer:

chubhunter [2.5K]2 years ago

4 0

Answer:

y = -x + 4

Step-by-step explanation:

(-1,5)...x1 = -1 and y1 = 5

(1,3)....x2 = 1 and y2 = 3

slope(m) = (y2 - y1) / (x2 - x1) = (3 - 5) / (1 - (-1) = -2 / (1 + 1) = -2/2 = -1

y = mx + b

slope(m) = -1

u can use either of ur points...I will use (1,3)...x = 1 and y = 3

now we sub and find b, the y int

3 = -1(1) + b

3 = -1 + b

3 + 1 = b

4 = b

ur equation is : y = -x + 4 <===

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So for this, we will be using synthetic division. To set it up, have the equation so that the divisor is -10 (since that is the solution of k + 10 = 0) and the dividend are the coefficients. Our equation will look as such:

<em>(Note that synthetic division can only be used when the divisor is a 1st degree binomial)</em>

-10 | 1 + 2 - 82 - 28
---------------------------

Now firstly, drop the 1:

-10 | 1 + 2 - 82 - 28
↓
-------------------------
1

Next, you are going to multiply -10 and 1, and then combine the product with 2.

-10 | 1 + 2 - 82 - 28
↓ - 10
-------------------------
1 - 8

Next, multiply -10 and -8, then combine the product with -82:

-10 | 1 + 2 - 82 - 28
↓ -10 + 80
-------------------------
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Next, multiply -10 and -2, then combine the product with -28:

-10 | 1 + 2 - 82 - 28
↓ -10 + 80 + 20
-------------------------
1 - 8 - 2 - 8

Now, since we know that the degree of the dividend is 3, this means that the degree of the quotient is 2. Using this, the first 3 terms are k^2, k, and the constant, or in this case k² - 8k - 2. Now what about the last coefficient -8? Well this is our remainder, and will be written as -8/(k + 10).

<u>Putting it together, the quotient is $k^2-8k-2-\frac{8}{k+10}$ </u>