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svetoff [14.1K]
3 years ago
7

What is the relationship among proportional relationships lines, rates of change, and slope?

Mathematics
2 answers:
tia_tia [17]3 years ago
5 0

First of all, let's define some concepts. In mathematics, proportional relationships happen when two values always change by the same multiple. That is, when one doubles, the other doubles as well. So, you can always reduce a proportional relationship to the same equation as follows:

y=kx \\ where \ k \ is \ the \ proportionality \ constant

This constant is also the <em>slope </em>of the straight line.

On the other hand, the average rate of change between any two points (x_{1},f(x_{1}) \ and \ (x_{2},f(x_{2}) is the slope of the line through the two points. The line through the two points is called the secant line and its slope is denoted as m_{sec}, so:

ARC=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}} \\ \\ \therefore ARC=\frac{Change \ in \ y}{Change \ in \ x}=m_{sec}

Finally, The slope of a nonvertical line is the number of units the line rises (or falls) vertically for each unit of horizontal change from left to right, so:

Slope=\frac{change \ in \ y}{change \ in \ x}=\frac{rise}{run}

<em>So, we can say that </em><em>the relationship</em><em> of these three concepts is that they all talk about the slope of a curve.</em>

sdas [7]3 years ago
3 0
<span><span>
It introduces the relationship between two variables and is called correlation. Proportionality or variation is state of relationship or correlation between two variables It has two types: </span>direct variation or proportion which states both variables are positively correlation. It is when both the variables increase or decrease together. On the contrary, indirect variation or proportion indicates negative relationship or correlation. Elaborately, the opposite of what happens to direct variation. One increases with the other variables, you got it, decreases. This correlations are important to consider because you can determine and identify how two variables relates with one another. Notice x = y (direct), y=1/x (indirect)</span>
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Can someone please help me in one of these!?
Anarel [89]

Answer:

9) y = -200x + 1200

11) slope = -2

15) $2,450

16) 9 days

Step-by-step explanation:

9) Given the two points from the graph:

Let (x₁, y₁) = (0, 1200)

(x₂, y₂) =  (1, 1000)

Substitute these values into the following slope formula:

m = (y₂ - y₁)/(x₂ - x₁)

m = (1000 - 1200)/(1 - 0)

m = -200/1

m = -200

The slope of the line is -200.

Next, we need to determine the y-intercept, which is the point on the graph where it crosses the y-axis. Upon observing the graph, it shows that the line crosses at point (0, 1200). The y-coordinate of this ordered pair is the value of the y-intercept, b = 1200.

Therefore, the linear equation in slope-intercept form is y = -200x + 1200.

<h3>11) Given the points, (5, -18) and (-4, 0): </h3>

Let (x₁, y₁) =(5, -18)

(x₂, y₂) =  (-4, 0)

Substitute these values into the following <u>slope formula</u>:

m = (y₂ - y₁)/(x₂ - x₁)

m = \frac{0 - (-18)}{-4 - 5} = \frac{0 + 18}{-9} = -2

Therefore, the slope of the line is -2.

<h3>15) Solve:</h3>

Given the fixed fee of $200, and the $150 per hour after the initial meeting:

We can represent these in slope-intercept form:

y = 150x + 200

y = total cost for the Attorney's services

x = number of hours worked.

The y-intercept in this given problem is $200, which represents the flat fee charged for the initial meeting. While the slope in this equation is $150, which is the hourly rate that an Attorney charges his clients after the initial meeting.

If an Attorney works for 15 hours, then:

Let x = 15, and substitute its value into the equation to find the total cost:

y = 150x + 200

y = 150(15) + 200

y = 2,250 + 200

y = 2,450

Therefore, a client will pay a total of $2,450 for an Attorney's 15 hours of work.

<h3>16) Solve: </h3>

Given the water level on a Lake of 165 inches after a rainstorm, and the water level's receding rate of 3 inches per day:

We can establish the following linear equation to model this given problem:

L = -3d + 165

Where:

L = represents the water level of the Lake

d = number of days that the water level recedes

In order to find the number of days it will take before the water level recedes to 84 inches:

Substitute the value of L = 84 into the equation:

L = -3d + 165

84 = -3d + 165

Subtract 165 from both sides:

84 - 165 = 3d + 165 - 165

-27 = -3d

Divide both sides by  -3:

\frac{-27}{-3} = \frac{-3d}{-3}

9 = d

Therefore, it will take 9 days for the water level to be at 84 inches.

7 0
3 years ago
Write the equation in slope-intercept form of the line that has a slope of -7/8 and contains the point (-4, 9).
lubasha [3.4K]

Answer:

The equation of the line is y = -7/8x + 11/2

Step-by-step explanation:

Since we have the slope and a point to start, we can use point-slope form to find the equation.

y - y1 = m(x - x1)

Use the slope for m and the point at (x1, y1). Then solve for y.

y - 9 = -7/8(x + 4)

y - 9 = -7/8x - 7/2

y = -7/8x + 11/2

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Answer is 39.62% 84 is 39.62% of 212. Let's find 39.62% of 212 212 x 39.62% 212 x 39.62/100 83.9944 Which is approximately equal to 84 So the answer is 39.62%
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What is the correct definition of the word bias? a. particular point of view b. a personal or unreasoned judgment c. to study in
wlad13 [49]

Answer:

b. a personal or unreasoned judgment

Step-by-step explanation:

The answer is B because bias is basically something or someone that you favor over anything or anyone else. Or what you belving in your own opion.

As an example, our strong bias in favor for the idea, or a test biased towards people who are excellent at math.

7 0
3 years ago
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