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3 years ago

Find the slope of the line passing through each of the following pairs of points. b (−3, 9), (−3, −5)

Mathematics

2 answers:

Kisachek [45]3 years ago

5 0

The formula of a slope:

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

We have:

$(-3,\ 9)\to x_1=-3,\ y_1=9\\(-3,\ -5)\to x_2=-3,\ y_2=9$

Substitute:

$m=\dfrac{-5-9}{-3-(-3)}=\dfrac{-14}{-3+3}=\dfrac{-14}{0}\ \ \ \boxed{!!!!!}$

Answer: The slope is indefinite

marusya05 [52]3 years ago

4 0

Hi there! :)

Step-by-step explanation:

$SLOPE=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}$

$\frac{(-5)-9}{(-3)-(-3)}=\frac{-5-9}{-3+3}=\frac{-14}{0}=0$

Undefined.

Slope is 0.

Final answer is 0.

Hope this helps!

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2 years ago

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prisoha [69]

Use two points from the graph to check if they are constant. In this case let’s use (0,50) & (2,58)

To find slope you have to do the following.

y2-y1 / x2-x1

Plug in the values, 58-50/2-0
This gives you 4.

When you use two other points, in this case (10,90) (20,130) you get a slope of 4.

This means the slope is 4.

We are trying to get an equation of y=mx+b.
We have slope already which is 4. So now we plug in y=4x + b

Now we need to find b. There is an equation to solve for b. Which is b=y1-m(x1)

But b is the y-intercept so there is already a B which is 50

So the table IS a linear equation and the equation is y=4x+50.

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3 years ago

Several students and adult chaperones are going on a field trip to the theater. Each student ticket cost $2 and each adult ticke

stiks02 [169]

The answer to this question would be: A. the number of adults

In this question, there are 4 times as many students as adults going on the trip. If we put it into a function where s= student and a=adult, then we could get one equation:
1. s=4a

Each student ticket cost $2 and each adult ticket cost $4. The total cost of the trip is $144. We also can get one equation for this
2. 2s+ 4a= 144

If you put the first equation into the second, you will get:
2s+4a= 144
2(4a)+4a= 144

The function is already similar with 2(4x)+4x but it uses a instead of x. Then x = a = number of adult

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2 years ago

Read 2 more answers

A denotes an mn matrix. Determine whether the statement is true or false. Justify your answer. The row space of AT is the same a

ziro4ka [17]

Answer: true

Step-by-step explanation:

For an m*n matrix, the column space of A will be a space formed by the lineal combination of all the columns of A.

column space = a1*c1 + a2*c2 + ...

where a1, a2, ... are scalars, and c1 is the vector of column 1.

Then we should write:

Column space = a1*(A₁₁, A₂₁, A₃₁, ...) + a2*(A₁₂, A₂₂, A₃₂, ...) + ...

Now, the transpose is defined as:

[At]₁₃ = A₃₁

Here i used the element with subindex 3 and 1, but is the same for every subindex.

Notice that if A is m*n, then [At] is n*m

Now, the row space of [At] will be, same as before.

Row space = b1*r1 + b2*r2 + ...

Where b1, b2, ... are scalars and the r's are the vector of each row.

= b1*( [At]₁₁ , [At]₁₂, [At]₁₃, ...) + b2*([At]₂₁, [At]₂₂, [At]₂₃, ...) + ...

Now we replace each term of the transpose by the associated element in the original matrix.

= b1*( A₁₁, A₂₁, A₃₁, ...) + b2*(A₂₁, A₂₂, ...) + ....

If we take:

b1 = a1, b2 = a2, b3 = a3, ...

We will have that the row space of [At] is the same as the column space of A.

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2 years ago

The ordered pairs in the table below represent a linear function.

GenaCL600 [577]

Answer:

$\displaystyle m=2$

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

Point (6, 2)

Point (9, 8)

Step 2: Find slope m

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

Substitute in points [Slope Formula]: $\displaystyle m=\frac{8-2}{9-6}$
[Fraction] Subtract: $\displaystyle m=\frac{6}{3}$
[Fraction] Divide: $\displaystyle m=2$

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2 years ago