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3 years ago

What is the slope of the line represented by the equation y = 6x - 12?

1 answer:

6 0

There are different types of equations of lines.
There are these three main forms, but I'll focus on just 2:

Slope-Intercept Form:
y = mx + b

Where,
"m" = slope
"b" = y-intercept

Point-Slope Form:
y - y1 = m(x - x1)

Where,
"m" = slope
"y1" = A y point on the graph
"x1" = A x point on the graph that correlates with the y value.

y = 6x - 12

Is in the same form of Slope-Intercept:

So,

y = 6x - 12

m = 6
b = -12

So our slope is,
6

Keep in mind if it was a fraction (Example: 6/5, then the slope is 6/5) the slope will be the entire fraction.

Also remember slope is the RISE over the RUN meaning it is the y value over the x value. So in this case we would go UP 6 and right 1 (because 6 is understood as 6/1).

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I need help fast

hram777 [196]

Answer:

On a coordinate plane, a line goes through (0, 3) and (2, 4) and another line goes through (0, 3) and (0.75, 0).

This answer almost coincide with option C. I suppose there was a mistype.

Step-by-step explanation:

The system of equations is formed by:

–x + 2y = 6

4x + y = 3

In the picture attached, the solution set is shown.

The first equation goes through (0, 3) and (2, 4), as can be checked by:

–(0) + 2(3) = 6

–(2) + 2(4) = 6

The second goes through (0, 3) and (0.75, 0), as can be checked by:

4(0) + (3) = 3

4(0.75) + (0) = 3

7 0

3 years ago

Read 2 more answers

Is 6:9 reater than less than or equal to 9:12

insens350 [35]

Answer:

less than

Step-by-step explanation:

6/9 is less than 9/12

6/9=.6666666666666666666666666

9/12=.75

.666666<.75

5 0

3 years ago

How do I do this homework???

Nonamiya [84]

Step-by-step explanation:

135

/ \

3. 45

/ \

3. 15

/ \

3. 5

250

/ \

10 .25

/\ / \

2 5. 5 5

351

/ \

3. 117

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3. 39

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3. 13

Hope it helps :)

5 0

4 years ago

What is the value of the expression when n = 3?<br> GO<br> - 2 n(5 + n-8-3n)

lukranit [14]

Answer:

Step-by-step explanation:

since n = 3

= -2n ( 5n+n-8-3n)

= -2 (3) ( 5+(3)-8-3(3) )

= -6 (5+3-8-9)

= -6 (5-5-9)

= -6 (-9)

= 54.

8 0

3 years ago

Let X and Y be discrete random variables. Let E[X] and var[X] be the expected value and variance, respectively, of a random vari

Ulleksa [173]

Answer:

(a) $E[X+Y]=E[X]+E[Y]$

(b) $Var(X+Y)=Var(X)+Var(Y)$

Step-by-step explanation:

Let X and Y be discrete random variables and E(X) and Var(X) are the Expected Values and Variance of X respectively.

(a)We want to show that E[X + Y ] = E[X] + E[Y ].

When we have two random variables instead of one, we consider their joint distribution function.

For a function f(X,Y) of discrete variables X and Y, we can define

$E[f(X,Y)]=\sum_{x,y}f(x,y)\cdot P(X=x, Y=y).$

Since f(X,Y)=X+Y

$E[X+Y]=\sum_{x,y}(x+y)P(X=x,Y=y)\\=\sum_{x,y}xP(X=x,Y=y)+\sum_{x,y}yP(X=x,Y=y).$

Let us look at the first of these sums.

$\sum_{x,y}xP(X=x,Y=y)\\=\sum_{x}x\sum_{y}P(X=x,Y=y)\\\text{Taking Marginal distribution of x}\\=\sum_{x}xP(X=x)=E[X].$

Similarly,

$\sum_{x,y}yP(X=x,Y=y)\\=\sum_{y}y\sum_{x}P(X=x,Y=y)\\\text{Taking Marginal distribution of y}\\=\sum_{y}yP(Y=y)=E[Y].$

Combining these two gives the formula:

$\sum_{x,y}xP(X=x,Y=y)+\sum_{x,y}yP(X=x,Y=y) =E(X)+E(Y)$

Therefore:

$E[X+Y]=E[X]+E[Y] \text{ as required.}$

(b)We want to show that if X and Y are independent random variables, then:

$Var(X+Y)=Var(X)+Var(Y)$

By definition of Variance, we have that:

$Var(X+Y)=E(X+Y-E[X+Y]^2)$

$=E[(X-\mu_X +Y- \mu_Y)^2]\\=E[(X-\mu_X)^2 +(Y- \mu_Y)^2+2(X-\mu_X)(Y- \mu_Y)]\\$Since we have shown that expectation is linear$\\=E(X-\mu_X)^2 +E(Y- \mu_Y)^2+2E(X-\mu_X)(Y- \mu_Y)]\\=E[(X-E(X)]^2 +E[Y- E(Y)]^2+2Cov (X,Y)$

Since X and Y are independent, Cov(X,Y)=0

$=Var(X)+Var(Y)$

Therefore as required:

$Var(X+Y)=Var(X)+Var(Y)$

7 0

3 years ago