write the equation of the line in point-slope slope-intercept and standard forms where the two points is (5,-6) and (6,-5). 20 points and brainliest to the best answer

Answer:

Slope-intercept form:   y = x  - 11

Standard form:   y - x = 11

Point-slope form:   y + 5 = (x - 6)

Step-by-step explanation:

Given the two points, (5, -6) and (6, -5):

We must first solve for the slope, as it will be used in the point-slope and slope-intercept forms.  

Let (x₁, y₁) =  (5, -6)

     (x₂, y₂) = (6, -5)

Substitute these values into the following slope formula:

[tex]\LARGE\mathsf{m = \frac {(y_2\: -\: y_1)}{(x_2\: -\: x_1)}}[/tex]

[tex]\LARGE\mathsf{m = \frac {-5\: -\: (-6)}{6\:-\:5}\:=\frac{-5\:+\:6}{ 1 } \:=\frac{1}{ 1 }}[/tex]

m = 1

Therefore, the slope of the line is 1.

Next, we must determine the y-intercept of the line. The y-intercept is the point on the graph where it crosses the y-axis, at point (0, b). In order to find the y-intercept, use one of the given points, (6, -5), and the slope, m = 1, and substitute into the slope-intercept form, y = mx + b:

y = mx + b

-5 = 1 (6) + b

-5 = 6 + b

Subtract 6 from both sides:

-5 - 6 = 6 - 6 + b

-11 = b

Therefore, the y-intercept is (0, -11), where b = -11.

Now that we have the value for the slope of the line, m = 1, and the y-intercept, b = -11, we could proceed in creating the linear equation in slope-intercept, point-slope, and standard forms.

Given our slope, m = 1, and the y-intercept, b = -11, we can express the linear equation in the following forms:

We could transform the slope-intercept form into the standard form:

Ax + By = C

where:

Transform the slope-intercept form into standard form.

Start by subtracting x from both sides of the equation:

y - x = x  - x - 11

y - x = -11  ⇒  This is the standard form where A = 1, B = -1, and C = -11.

Use one of the given points, (6, -5) and substitute into the point-slope form:

y - y₁ = m(x - x₁)

y - (-5) = 1(x - 6)

y + 5 = (x - 6)   ⇒  This is the point-slope form.

Name the angle pair: ∠5 and ∠8


alternate exterior angles

corresponding angles

same side interior angles

same side exterior angles

vertical angles

alternate interior angles

linear pair

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6. There are approximately 210 M&M’s in a 7-ounce bag of M&M’s.

a. Write and solve a proportion that you can use to find the number of
M&M’s in a 3-ounce bag.

b. What is the number of M&M’s per ounce?

c. Approximately how many ounces does each M&M weigh? Round to the nearest hundredth.

15 points <3......................

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What percent of questions did Amiya answer correctly on her last exam?

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MAY YALL HELP MEH?????? I WOULD DO MY SELF BUT YEAHH

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The options are in the picture ⬆️​

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ILL GIVE BRAINLEIST
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B. The rate of change is the number of grams gained per day, and the initial value is the starting weight.

C. The rate of change is the starting weight, and the initial value is the number of grams gained per day.

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The dimensions of a rectangular prism are shown below:

Length: 1 1/2 feet
Width: 1 foot
Height: 2 1/2 feet
The lengths of the sides of a small cube are 1/2 foot each.

Part A: How many small cubes can be packed in the rectangular prism? Show your work.

Part B: Use the answer obtained in part A to find the volume of the rectangular prism in terms of the small cube and a unit cube.


Correct answers: Brainliest and a Thanks!
Incorrect answers: 1-2 star (Make sure you know the answers please!)
Improper answers: Reported and 1 star (No links!!)

-4(-u-2y+6)
please answer I will give a Brainliest for the first person

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6 times the sum of a number and 5

options:

6(n+5)

5n + 6

5(n+6)

6 + 5n

how do you do this 20 pts.

PLS HELP THIS IS RLLY HARD FOR ME
The two seventh grade classes at VSH Middle School collected the most box tops for a school
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This one is one with better lighting sorry about the last one, anyways like I said I did the first two i don’t know if they’re right, this is honestly confusing for me so pls help me this homework counts as an important grade

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By how much does the ice sheet's thickness decrease every 6 weeks?

____ meters