Ask question

Ask question

All categories

3 years ago

7

What is the equation of the line that passes through (6,4) and (4,1)

1 answer:

Murrr4er [49]3 years ago

3 0

Answer:

y = 3/2*x - 5

Step-by-step explanation:

Lets say that P1=(6,4) and P2=(4,1) and that the form of the equation must be y=m*x+b where m is the slope and b the independent variable. Then having two given points we can use the slope formula to find the slope value as:

P1=(x1,y1) and P2=(x2,y2)

slope formula ---> m=(y2-y1)/(x2-x1)

Replacing the given points ---> m=(1-4)/(4-6) = 3/2

then replacing the slope value obtained:

y = 3/2*x + b

Now lets find the value of b. For this we have to replace in the equation a point it can be P1 or P2, i will replace P2:

1 = 3/2*4 + b

1 = 6 + b

1 - 6 = b

-5 = b

therefore the line equation is:

y = 3/2*x - 5

You might be interested in

Simplify: (–7) • (8) – (4) • (–2) A. 58 B.16 C.–30 D.–48

jeka94

D. -48
Put it into your calculator exactly how it is shown up above and you will get the correct answer. Your calculator automatically knows the order of operations.

4 0

3 years ago

Callie has a new kitten. They can weigh 3 pounds less than half the weight of Callie‘s cat. Together the cat and kitten weigh 18

gavmur [86]

Answer:

The weight of cat is <u>14 pounds</u> and the weight of kitten is <u>4 pounds</u>.

Step-by-step explanation:

Given:

Callie has a new kitten. It can weigh 3 pounds less than half the weight of Callie‘s cat. Together the cat and kitten weigh 18 pounds.

Now, to find the weight of each animal:

Let the cat's weight be $x.$

And the kitten weight = $\frac{x}{2} -3$

Total weight of cat and kitten = 18 pounds.

Now, to set an equation to get the weight of each animal:

$(x)+(\frac{x}{2}-3)=18$

$x+\frac{x}{2} -3=18$

$\frac{2x+x-6}{2} =18$

$\frac{3x-6}{2} =18$

<em>Multiplying both sides by 2 we get:</em>

<em /> $3x-6=36$ <em />

<em>Adding both sides by 6 we get:</em>

<em /> $3x=42$ <em />

<em>Dividing both sides by 3 we get:</em>

<em /> $x=14\ pounds.$ <em />

<em>The weight of cat = 14 pounds.</em>

Substituting the value of $x$ to get the kitten's weight:

$\frac{x}{2} -3\\\\=\frac{14}{2}-3\\\\=7-3\\\\=4.$

<em>The kitten's weight = 4 pounds.</em>

Therefore, the weight of cat is 14 pounds and the weight of kitten is 4 pounds.

7 0

3 years ago

The formula Y=X⁴-4X³+3X² is growing?

miskamm [114]

Answer:

The best way to know weather the formula y=x⁴-4x³+3x² is growing or not, is by graphing it.

As you can see in the attached picture:

For -inf<x< 0 the graph decreases.
For 0<x<0.634 the graph is growing
For 0,634<x<2.366 the graph decreases
For 2.366<x<+inf the graph is growing.

Therefore, the polynomial grows in the intervals stated before.

6 0

3 years ago

A club raised 80% of its goal for a charity. The club raised $1076. What was the goal?

4vir4ik [10]

Answer:

860.8

Step-by-step explanation:

6 0

3 years ago

Find the inverse of the function. Show work. <br> g(x)= - 3/x-2 +2

4vir4ik [10]

Answer:

$\displaystyle g^{-1}(x)=\frac{-7+2x}{x-2}$

Step-by-step explanation:

We are given the function:

$\displaystyle g(x)=-\frac{3}{x-2}+2$

Let's find the inverse of g.

Call y=g(x):

$\displaystyle y=-\frac{3}{x-2}+2$

We need to solve for x. Multiply both sides by x-2 to eliminate denominators:

$y(x-2)=-3+2(x-2)$

Operate:

$yx-2y=-3+2x-4$

Collect the x's to the left side and the rest to the right side of the equation:

$yx-2x=-3-4+2y$

Factor the left side and operate on the right side:

$x(y-2)=-7+2y$

Solve for x:

$\displaystyle x=\frac{-7+2y}{y-2}$

Interchange variables:

$\displaystyle y=\frac{-7+2x}{x-2}$

Call y as the inverse function:

$\boxed{\displaystyle g^{-1}(x)=\frac{-7+2x}{x-2}}$

5 0

3 years ago