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3 years ago

Which line contains the point (1,-3)

1 answer:

4 0

There are infinitely many lines that have the point (1,-3).

A line can be expressed as:

y=mx+b, where m=slope and b=y-intercept..

Our only restriction is that it passes through (1,-3) so

-3=1m+b

So as long as the sum of the slope and the y-intercept is equal to -3, that is one of the infinite number of lines that passes through (1, -3)

So we could also say b=-3-m then our infinite lines are:

y=mx-3-m, now any real value of m creates a specific line that passes through the point. ie the first few are

y=x-4, y=2x-5, y=3x-6 or even y=x√2-3-√2

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2. Given a directed line segment with endpoints A(3, 2) and B(6, 11), what is the point that

KATRIN_1 [288]

Answer:

The point of division is (5 , 8)

Step-by-step explanation:

* Lets explain how to solve the problem

- If point (x , y) divides the line whose endpoints are $(x_{1},y_{1})$

and $(x_{2},y_{2})$ at ratio $m_{1}:m_{2}$ , then

$x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$ and

$y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

* Lets solve the problem

- The directed line segment with endpoints A (3 , 2) and B (6 , 11)

- There is a point divides AB two-thirds from A to B

∵ The coordinates of the endpoints of the directed line segments

are A = (3 , 2) and B = (6 , 11)

∴ $(x_{1},y_{1})$ is (3 , 2)

∴ $(x_{2},y_{2})$ is (6 , 11)

∵ Point (x , y) divides AB two-thirds from A to B

- That means the distance from A to the point (x , y) is 2/3 from

the distance of the line AB, and the distance from the point (x , y)

to point B is 1/3 from the distance of the line AB

∴ $m_{1}:m_{2}$ = 2 : 1

∵ $x=\frac{(3)(1)+(6)(2)}{2+1}=\frac{3+12}{3}=\frac{15}{3}=5$

∴ The x-coordinate of the point of division is 5

∵ $y=\frac{(2)(1)+(11)(2)}{2+1}=\frac{2+22}{3}=\frac{24}{3}=8$

∴ The y-coordinate of the point of division is 8

∴ The point of division is (5 , 8)

6 0

3 years ago

You had $20 to spend on seven avocados. After buying them you had $6. How much did each avocado cost?

mestny [16]

They each cost 2 dollars

8 0

2 years ago

Read 2 more answers

5) Derek was surfing through the internet for a good deal on t-shirts. Help Derek find the

AlladinOne [14]

Answer:

The first one

Step-by-step explanation:

To figure out which one is the best deal, for each one how much one t-shirt costs.

First deal:

3 t-shirts for $28.95

To figure out how much money one t-shirt would cost, you divide $28.95 by 3.

1 t-shirt = 28.95/3 = $9.65.

Second deal:

4 t-shirts for $39

Same thing as the last one, except since there are 4 t-shirts you divide $39 by 4.

1 t-shirt = 39/4 = $9.75

Third deal:

5 t-shirts for $49.95

This time you will divide 49.95 by 5.

1 t-shirt = 49.95/5 = $9.99

The last step is to compare the three deals, and since you are trying to find the one that costs the least you can see that the first deal is the best one, because $9.65 per shirt is cheaper than $9.75 and $9.99

5 0

3 years ago

If f(x)= 3x + 4, then what is f(-2)

iren [92.7K]

Answer:

f ( - 2 ) = - 2

Step-by-step explanation:

Step 1:

f ( x ) = 3x + 4 Equation

Step 2:

f ( - 2 ) = 3 ( - 2 ) + 4 Input x value

Step 3:

f ( - 2 ) = - 6 + 4 Combine Like Terms

Answer:

f ( - 2 ) = - 2 Combine Like Terms

Hope This Helps :)

6 0

3 years ago

Image explains everything worth alot of points! Thanks

asambeis [7]

Answer:

Step-by-step explanation:

55/5 = 11

7 0

2 years ago