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3 years ago

Calculate the slope of the line given the points (2,1) and (1,-4)

Mathematics

2 answers:

Dmitrij [34]3 years ago

8 0

The equation for the slope of a line is:

y2-y1/x2-x1

So:

-4-1/1-2 = -5/-1 =5

The slope of the line is 5.

ANEK [815]3 years ago

7 0

Answer:

$\Huge \boxed{5}$

Step-by-step explanation:

Slope formula:

$\displaystyle \frac{y_2-y_1}{x_2-x_1}$

$\displaystyle \frac{(-4)-1}{1-2}=\frac{-5}{-1}=5$

$\Large\textnormal{Therefore, the slope is 5, and the correct answer is 5.}$

$\Large\textnormal{Hope this helps!}$

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The denarius was a unit of currency in ancient rome. Suppose it costs the roman government 101010 denarii per day to support 444

givi [52]

<u>the correct question is</u>

The denarius was a unit of currency in ancient rome. Suppose it costs the roman government 10 denarii per day to support 4 legionaries and 4 archers. It only costs 5 denarii per day to support 2 legionaries and 2 archers. Use a system of linear equations in two variables. Can we solve for a unique cost for each soldier?

Let

x-------> the cost to support a legionary per day

y-------> the cost to support an archer per day

we know that

4x+4y=10 ---------> equation 1

2x+2y=5 ---------> equation 2

If you multiply equation 1 by 2

2*(2x+2y)=2*5-----------> 4x+4y=10

equation 1 and equation 2 are the same

The system has infinite solutions-------> Is a consistent dependent system

therefore

<u>the answer is</u>

We cannot solve for a unique cost for each soldier, because there are infinite solutions.

5 0

3 years ago

Find the equation of the line that passes through the following points. Write the equation in slope-intercept form.

ra1l [238]

Answer:

The equation in the slope-intercept form will be:

y = 1/4x - 7

Step-by-step explanation:

Given the points

(-4.-8)

(-8, -9)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-4,\:-8\right),\:\left(x_2,\:y_2\right)=\left(-8,\:-9\right)$

$m=\frac{-9-\left(-8\right)}{-8-\left(-4\right)}$

$m=\frac{1}{4}$

We know that the slope-intercept of line equation is

$y=mx+b$

where m is the slope and b is the y-intercept

substituting m = 1/4 and the point (-4, -8) to find the y-intercept 'b'

y = mx+b

-8 = 1/4(-4)+b

-8 = -1 + b

b = -8+1

b = -7

so the y-intercept = b = -7

substituting m = 1/4 and b = -7 in the slope-intercept form of line equation

y = mx+b

y = 1/4x + (-7)

y = 1/4x - 7

Thus, the the equation in slope-intercept form will be:

y = 1/4x - 7

6 0

3 years ago

Common factors of 28 and 40

Nady [450]

28: 1, 2, 4, 7, 14, 28

40: 1, 2, 4, 5, 8, 10, 20, 40

The common factors are 1, 2, and 4.

You can use a factor rainbow to help you find the factors (:

7 0

3 years ago

Suppose that a typical household in the United States has an average after-tax income of $41,100. The circle graph below represe

Zarrin [17]

Answer:

9% + 5%

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

In 2 mins., a conveyor belt moves 300 lbs. Of recycle aluminum from delivery truck to a storage area. A smaller belt moves the s

kodGreya [7K]

Answer:

1.8 minutes or 108 seconds

Step-by-step explanation:

The question tells us that the larger belt moves 300 lbs in 2 mins. And this is equal to 150 lb per minute

The question also tells us that a smaller belt moves the same quantity of 300 lbs in 18 mins. And this is equal to an average of 16.667 lb per min.

Both belts will move at a rate of 166.667 lb per min.

So it will take them 300 / 166.667 = 1.8 min or 108 s.

Therefore, the answer is 1.8 min

6 0

3 years ago