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3 years ago

Find the slope of the line that passes through the points (0,-4) and (10,3)

Mathematics

1 answer:

expeople1 [14]3 years ago

8 0

Answer:

$\displaystyle m = \frac{7}{10}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Coordinates (x, y)
Slope Formula: $\displaystyle m = \frac{y_2-y_1}{x_2-x_1}$

Step-by-step explanation:

Step 1: Define

Identify

Point (0, -4)

Point (10, 3)

Step 2: Find slope m

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

Substitute in points [Slope Formula]: $\displaystyle m = \frac{3--4}{10-0}$
[Fraction] Subtract: $\displaystyle m = \frac{7}{10}$

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2 years ago

8. Given: PQR and TSR are right triangles,

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The answer is below

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. Types of triangles are scalene, right angled, isosceles, equilateral.

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2 years ago

Let T: set of real numbers R Superscript nℝnright arrow→set of real numbers R Superscript mℝm be a linear transformation, and

Klio2033 [76]

Answer:

$\{T(v_1), T(v_2), T(v_3)\}$ is linearly dependent set.

Step-by-step explanation:

Given: $\{v_1,v_2,v_3\}$ is a linearly dependent set in set of real numbers R

To show: the set $\{T(v_1), T(v_2), T(v_3)\}$ is linearly dependent.

Solution:

If $\{v_1,v_2,v_3,...,v_n\}$ is a set of linearly dependent vectors then there exists atleast one $k_i:i=1,2,3,...,n$ such that $k_1v_1+k_2v_2+k_3v_3+...+k_nv_n=0$

Consider $k_1T(v_1)+k_2T(v_2)+k_3T(v_3)=0$

A linear transformation T: U→V satisfies the following properties:

1. $T(u_1+u_2)=T(u_1)+T(u_2)$

2. $T(au)=aT(u)$

Here, $u,u_1,u_2$ ∈ U

As T is a linear transformation,

$k_1T(v_1)+k_2T(v_2)+k_3T(v_3)=0\\T(k_1v_1)+T(k_2v_2)+T(k_3v_3)=0\\T(k_1v_1+k_2v_2+k_3v_3)=0\\$

As $\{v_1,v_2,v_3\}$ is a linearly dependent set,

$k_1v_1+k_2v_2+k_3v_3=0$ for some $k_i\neq 0:i=1,2,3$

So, for some $k_i\neq 0:i=1,2,3$

$k_1T(v_1)+k_2T(v_2)+k_3T(v_3)=0$

Therefore, set $\{T(v_1), T(v_2), T(v_3)\}$ is linearly dependent.

6 0

3 years ago

Find the slope intercept (9,5),(7,-11) y=

grin007 [14]

Answer:

y=8x-67

Step-by-step explanation:

So the question is what is the equation for the following two coordinate points?

Well to start off what is the formula? The formula is called the linear equation. Which is y=mx+b. What does these letters or "variables" mean or represent?! Welp, m stands for the slope, which is "Δy over Δx." Some people call say "the change of y over x." I call it the rise over run. So it is saying y over x. The b in the linear equation is the y-intercept. The y-intercept is when the line crosses the y-axis.

With that being said, let's find the slope. But how? Well with the Δy over Δx. The formula is y₂-y₁ over x₂-x₁. With the two coordinate points we can label them.

y₂=5

y₁=(-11)

x₂=9

x₁= 7

Now let set it up into the equation of y over x

Slope = 5- (-11) = 5 + 11 = 16 = 8

9-7 9-7 2

So we now have the slope! Which is 8! So put that into the linear equation!

y=8x+b

Next, we need to find b, the y-intercept! How do we do that well, we can figure it out by one of the coordinate points! Let use the (7, -11) point for example! Remember, x= 7 and y= (-11)

(-11) = 8(7) + b

(-11) = 56 + b

-56 -56

-67 = b

We now have b, which is negative 67! So we need to put all the information we have found into the linear equation!

y=8x-67

6 0

3 years ago