Written in slope-intercept form, the equation x + 2y = 4 is 2y = -x + 4 y = -1/2x + 4 y = -1/2x + 2

The slope-intercept form of the equation is

The given equation is:

x  +  2y   =  4

The slope-intercept form of the equation of a line is:

y   =  mx  +  c

where m represents the slope

c represents the y-intercept

Express the equation x + 2y = 4 in the form y = mx + c

x   +  2y   =  4

2y  =  -x  +  4

Divide through by 2

Therefore, the slope-intercept form of the equation is

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x + 2y = 4

Slope intercept form is y = mx + b where m = slope and b = y-intercept.

In this case

x + 2y = 4

2y = -x + 4

 y = -1/2 x + 2

Answer

Slope intercept form: y = -1/2 x + 2

a)

P(Y=1|X=2) = p(2,1) = 0.1

P(Y=2|X=2) = p(2,2) = 0

P(Y=3|X=2) = p(3,2) = 0.1

b)

NO

c)

P(X+Y>3) = 0.55

P(XY=4) = 0

P(XY>2) = 0.55

Step-by-step explanation:

The joint probability table is given in the picture attached

a)

P(Y=1|X=2) = p(2,1) = 0.1

P(Y=2|X=2) = p(2,2) = 0

P(Y=3|X=2) = p(3,2) = 0.1

b)

Two events A and B are independent if, and only if,

P(A|B) = P(A) and P(B|A) = P(B)

X and Y are not independent since

P(Y=1|X=2) = p(2,1) = 0.1

whereas

P(Y=1) = 0.5

so we can see

P(Y=1|X=2)≠ P(Y=1)

c)

P(X+Y>3) = p(1,3)+p(2,2)+p(2,3)+p(3,1)+p(3,2)+p(3,3)=

0.05+0+0.1+0.1+0.05+0.25 = 0.55

P(XY=4) = p(2,2) = 0

P(XY>2) = p(1,3)+p(2,2)+p(2,3)+p(3,1)+p(3,2)+p(3,3) = 0.55