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3 years ago

Find the equation of a line with the given points.(put your answers in the form y=mx+b)(6,2)(5,5)

Mathematics

2 answers:

Nesterboy [21]3 years ago

6 0

The slope-intercept form: y= mx + b

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (6, 2) and (5, 5). Substitute:

$m=\dfrac{5-2}{5-6}=\dfrac{3}{-1}=-3$

Therefore we have y = -3x + b.

Put the coordinates of the point (5, 5) to the equation:

5 = -3(5) + b

5 = -15 + b add 15 to both sides

20 = b

<h3>Answer: y = -3x + 20</h3>

igomit [66]3 years ago

5 0

Answer:

y = -3x + 20

Step-by-step explanation:

(a) Slope

The point-slope formula for a straight line is

y₂ - y₁ = m(x₂ - x₁) Insert the points

2 - 5 = m(6 - 5)

-3 = m×1

m = -3

=====

(b) y-intercept

y₂ - y₁ = m(x₂ - x₁)

y₂ - 5 = -3(x₂ - 5) Remove parentheses

y₂ - 5 = -3x₂ - 15 Add 5 to each side

y = -3x + 20

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Answer:

3n^2 - 5n - 28

Step-by-step explanation:

(n - 4)(3n + 7)

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2 years ago

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Determine graphically if each function is even,odd,or neither.if even or odd state the symmetry

barxatty [35]

Answer:

graphically :

The graph is symmetrical about the origin.

Then it represents an odd function.

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The origin is a center of symmetry.

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1 year ago

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Help with 5b please . thank you.

Allushta [10]

Answer:

See explanation

Step-by-step explanation:

We are given f(x)=ln(1+x)-x+(1/2)x^2.

We are first ask to differentiate this.

We will need chain rule for first term and power rule for all three terms.

f'(x)=(1+x)'/(1+x)-(1)+(1/2)×2x

f'(x)=(0+1)/(1+x)-(1)+x

f'(x)=1/(1+x)-(1)+x

We are then ask to prove if x is positive then f is positive.

I'm thinking they want us to use the derivative part in our answer.

Let's look at the critical numbers.

f' is undefined at x=-1 and it also makes f undefined.

Let's see if we can find when expression is 0.

1/(1+x)-(1)+x=0

Find common denominator:

1/(1+x)-(1+x)/(1+x)+x(1+x)/(1+x)=0

(1-1-x+x+x^2)/(1+x)=0

A fraction can only be zero when it's numerator is.

Simplify numerator equal 0:

x^2=0

This happens at x=0.

This means the expression,f, is increasing or decreasing after x=0. Let's found out what's happening there. f'(1)=1/(1+1)-(1)+1=1/2 which means after x=0, f is increasing since f'>0 after x=0.

So we should see increasing values of f when we up the value for x after 0.

Plugging in 0 gives: f(0)=ln(1+0)-0+(1/2)0^2=0.

So any value f, after this x=0, should be higher than 0 since f(0)=0 and f' told us f in increasing after x equals 0.

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2 years ago

Joseph owns a hot dog stand and sells specialized hot dogs. He charges $1.50 for a plain hot dog and then an additional $0.50 fo

Lilit [14]

Hot Dog Stand

Let

C--------> total cost of the hot dog

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we know that

$C=0.5x+1.5$

where

The slope of the linear equation is equal to $0.5\frac{\$}{topping}$

The y-coordinate of the y-intercept of the linear function is equal to $\$1.5$

That means -------> This is the cost of the hot dog without topping

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Let

C--------> total cost of the hamburger

x-------> is the number of toppings

we know that

$C=0.25x+2.50$

where

The slope of the linear equation is equal to $0.25\frac{\$}{topping}$

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That means -------> This is the cost of the hamburger without topping

therefore

the answer is

The linear equation of the hamburger cost is equal to

$C=0.25x+2.50$

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Answer:

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