How are key features of a linear function identified and interpreted from an equation?

Take 2 points

[tex]\\ \sf\longmapsto m=\dfrac{12-10}{2-1}=2[/tex]

[tex]\\ \sf\longmapsto y=mx+b[/tex]

[tex]\\ \sf\longmapsto 10=2(1)+b[/tex]

[tex]\\ \sf\longmapsto b=8[/tex]

Function:-

[tex]\\ \sf\longmapsto f(x)=2x+8[/tex]

Answer:

Brooke and Tony

Step-by-step explanation:

multiply by 4 Brooke got 64 Tony got 68.

Answer:

Step-by-step explanation:

250000 - 1500s < 30000 + 1000s

           220000 < 2500s

                     88 < s

                       s > 88 years

which is a very long time for populations trends to remain constant as this question assumes.

Answer:

113

Step-by-step explanation:

supplementray means 180-67=113

113

The diagonal line is a straight line which means when another straight line passes through it, both sides will add up to 180

Answer:

$0.13 per lb

Step-by-step explanation:

The slope of a line between these two points is 0.13.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given that A hamster weighs half a pound and costs $2 per week to feed.

Labrador Retriever weighs 62.5 pounds and costs $10 per week to feed.

Let x be the weigh and y be the feed cost.

The two points of lines are (0.5, 2) and (62.5, 10)

m=10-2/62.5-0.5

m=0.13

Hence, the slope of a line between these two points is 0.13.

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Answer:

P (1+r÷100)^n

27000000(1+6.21 ÷ 100)^1

27000000.06

not sure about it though

[tex]5 - 4x < 95 \\ - 4x < 95 - 5 \\ - 4x = 90 \\ x = - \frac{90}{4} \\ \boxed{ x = - \frac{45}{2} }[/tex]

38 i ised my brain i think

_________

[tex] \: [/tex]

[tex] {8}^{ - 4} \times {8}^{6} x[/tex]

[tex] {8}^{ - 4 + 6} = x[/tex]

[tex] {8}^{6 - 4} = x[/tex]

[tex] {8}^{2} = x[/tex]

[tex]64 = x[/tex]

Soo, answer for question [tex]8^(-4) × 8^6 = 8^2[/tex]

Answer:a) 16 3/4 - 19 4/5 liters/min

b) (16 3/4 - 19 4/5) / 4 liters

c) The level of water will drop.

Step-by-step explanation:

Answer:

False

or

3951

Step-by-step explanation:

F(m) represents an equation that when the "m" is changed within the parenthesis, all the m's in the equation change as well. The function determines the value of the equation.

In this case, "m = 6" or in basic terms:

f(6) = m^5 + 3m^4 - 21m^3 - 12m^3 - 12m^2 = 31m - 33

Replace all m's with 6.

[tex]f(6) = (6)^5 + 3(6)^4 - 21(6)^3 - 12(6)^3 - 12(6)^2 = 31(6) - 33[/tex]

And do the exponents + coefficients.

6^5 = 7776

3(6^4) = 3888

-21(6)^3 = -4536

-12(6)^3 = -2592

-12(6)^2 = -432

31(6) = 186

-33 = -33

Our final equation is:

7776 + 3888 - 4536 - 2592 - 432 = 186 - 33

Add/subtract all together:

4104 = 153

Now because of your question being quite vague, there could be two ways of answering.

One: Determining whether the equation is true or false, which in this case. 4104 does indeed not equal 153, therefore making it false.

Two: Getting one single number, which we would have to subtract 153 from both sides to get the answer:

4104 - 153 = 153 - 153

[3951]

Answer:

1/6

Step-by-step explanation:

Answer:

4.8 miles

Step-by-step explanation:

Use proportions.

Answer:

9

Step-by-step explanation:

Answer:

Distributive property.

Step-by-step explanation:

Answer:

49 degrees

Step-by-step explanation:

Answer:

m<E = 49°

Step-by-step explanation:

Using the straight angle theorem, we can add the angles measuring 63, 68, and the angle above the 68(let's call it x) add to 180. We can write an equation:

63 + 68 + x = 180

This means:

x = 49

Angle x is alternate interior to angle E, meaning the two are congruent and have the same measure. This means m<E = 49

Answer:

-99%

Step-by-step explanation:

Since it is going down, it'll be negative.

8,000 - 80 = 7,920

7,920 / 8,000 = 0.99

0.99 x 100 = 99%

-99%

(they might be asking for just 99% though too!)

Have a nice day!

   I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

dun dun dunnnnnnnnnn

Answer:

(5,0)

Step-by-step explanation:

Switch the second equation around so it matches up with the first one :

4x-6y = 20

Then solve by elimination :

-2 (2x-3y = 10) = -4x+6y = -20

-4x+3y = -20

+ 4x-6y = 20

--------------------

-3y = 0

y = 0

Plug y as 0 into one equation :

2x-3(0) = 10

2x = 10

x = 5

Your solution would be (5,0) .

Answer:

20.15

Step-by-step explanation:

Answer:

20.15

Step-by-step explanation:

Answer:

I believe the answer is 341 hope this helps

Answer:

4

Step-by-step explanation:

Answer: Hi How are you doing

Step-by-step explanation:

Hi Hi Hi Hi Hi

Answer:

11

Step-by-step explanation:

a number squared is just a number that is multiplied by itself

so [tex]11^{2}[/tex] is just saying 11×11

[tex]\sqrt{121}[/tex]      given

[tex]\sqrt{11^{2} }[/tex]      changed to exponential form

  [tex]11[/tex]        simplify

Answer:

Step-by-step explanation:

9 * 11 = 99 dollars for adults.  16 * 5.50 = 88 dollars for kids.

Togther it would be 99 + 88 = 187

(A)

Step-by-step explanation:

To be able to compare the growth rates of these two people, we need to develop an equation to describe Ioana's growth history, just like Valentin did.

Let [tex]P_1(5, 102)[/tex] and [tex]P_2(10, 127).[/tex] Using the equation for the slope of a linear function,

[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

and this will represent the growth rate for Ioana. The slope in Valentin's equation also represents the growth rate. Using the values of the points that we picked, we get

[tex]m = \dfrac{127 - 102}{10 - 5} = \dfrac{25}{5} = 5[/tex]

The slope-intercept form of the equation that describes Ioana's growth can be written as

[tex]h_I = 5(a - 5) + b[/tex]

Note that we used (a - 5) instead of the usual variable a because the twins started recording their heights at the age of a = 5. Next, we need to figure out b, essentially Ioana's height at age 5. From the table, we can see that that b = 102. Hence, the equation for Ioana's height is

[tex]h_I = 5(a - 5) + 102[/tex]

Let's compare this with Valentin's equation for his height:

[tex]h_V = 4.5(a - 5) + 104[/tex]

We can see here that the slope for Ioana's equation is larger than Valentin's, which means that Ioana's growth rate is faster than that of Valentin, even though Valentin was taller when they first started.

The relationship between the x and y variables in the scatter plot is

approximately linear.

(a) Increase in the y-variable follows from an increase in the x-variable

(b) The regression coefficient is approximately 0.9465

(c) The slope of the regression line is 2.5

(d) The equation of the regression line is approximately; y = 2.5·x + 10.5

(e) If x = 25, the value of y is 73

Reasons:

(a) From the attached graph, we have;

The increase in the x-variable gives a corresponding increase in the y-

variable.

(b) The correlation coefficient is given by plotting the given points using

MS Excel and finding the regression line, from which we have;

The regression coefficient is R ≈ √(0.8958) ≈ 0.9465

(c) The slope of the regression line is given by the slope of the line with

points (7, 28), and (9, 33), as follows;

[tex]Slope = \dfrac{33 - 28}{9 - 7} = 2.5[/tex]

The slope of the regression line is approximately 2.5

(d) Using the slope, m = 2.5, we get;

Equation of regression line, is y - 33 = 2.5·(x - 9)

Which gives;

y - 33 = 2.5·(x - 9) = 2.5·x - 22.5

y = 2.5·x - 22.5 + 33 =

The equation of the line is; y = 2.5·x + 10.5

(e)  If x = 25, we have;

y = 2.5 × 25 + 10.5 = 73

Therefore, if x = 25, y = 73

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