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3 years ago

What is the slope of the line passing through the point (2,1) and the origin ?

Mathematics

1 answer:

liraira [26]3 years ago

6 0

Answer:

$m=\frac{1}{2}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Slope Formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Step-by-step explanation:

Step 1: Define

Random Point (2, 1)

Origin (0, 0)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m.

Substitute [SF]: $m=\frac{0-1}{0-2}$
Subtract: $m=\frac{-1}{-2}$
Simplify: $m=\frac{1}{2}$

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3 years ago

Solve: -4x-8x+17=23 check solution

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Answer:

x = -1/2

Step-by-step explanation:

To solve the equation, we first need to combine like terms:

$-12x+17=23$

Simplify further:

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Divide by -12 on both sides to get:

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To check the solution, plug x back into the original equation and check if we get the correct answer:

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3 years ago

If PQ=8 and Q lies at -13 where could P be located?

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Answer:

In the given figure the point on segment PQ is twice as from P as from Q is. What is the point? Ans is (2,1).

Step-by-step explanation:

There is really no need to use any quadratics or roots.

( Consider the same problem on the plain number line first. )

How do you find the number between 2 and 5 which is twice as far from 2 as from 5?

You take their difference, which is 3. Now splitting this distance by ratio 2:1 means the first distance is two thirds, the second is one third, so we get

4=2+23(5−2)

It works completely the same with geometric points (using vector operations), just linear interpolation: Call the result R, then

R=P+23(Q−P)

so in your case we get

R=(0,−1)+23(3,3)=(2,1)

Why does this work for 2D-distances as well, even if there seem to be roots involved? Because vector length behaves linearly after all! (meaning |t⋅a⃗ |=t|a⃗ | for any positive scalar t)

Edit: We'll try to divide a distance s into parts a and b such that a is twice as long as b. So it's a=2b and we get

s=a+b=2b+b=3b

⇔b=13s⇒a=23s

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