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DedPeter [7]
3 years ago
9

What is the point-slope form of a line that has a slope of –4 and passes through point (–3, 1)?

Mathematics
2 answers:
dimaraw [331]3 years ago
8 0

Answer:

y - 1 = - 4(x + 3)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 4 and (a, b) = (- 3, 1), hence

y - 1 = - 4(x - (- 3)), thus

y - 1 = - 4(x + 3) ← in point- slope form

dybincka [34]3 years ago
7 0

Answer:

y-1=-4(x+3)

Step-by-step explanation:

Given: A line has a slope of -4 and the line passes through a point (-3, 1).

To find: The point-slope form of this line.

Solution:

We know, the point-slope form of a line can be given as

y-y_{1}=m(x-x_{1} )

Here, m is the slope of the line, and (x_{1}, y_{1}) is the point through which it passes.

The slope of the line is -4, and the point is (-3, 1).

So, m=-4, x_{1} =-3, and y_{1} =1.

Now, putting the values in the equation, we get

y-1=-4(x-(-3))

y-1=-4(x+3)

Therefore, the point-slope form of the line is y-1=-4(x+3).

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A college student is taking two courses. The probability she passes the first course is 0.73. The probability she passes the sec
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b) No, it's not independent.

c) 0.02

d) 0.59

e) 0.57

f) 0.5616

Step-by-step explanation:

To answer this problem, a Venn diagram should be useful. The diagram with the information of Event 1 and Event 2 is shown below (I already added the information for the intersection but we're going to see how to get that information in the b) part of the problem)

Let's call A the event that she passes the first course, then P(A)=.73

Let's call B the event that she passes the second course, then P(B)=.66

Then P(A∪B) is the probability that she passes the first or the second course (at least one of them) is the given probability. P(A∪B)=.98

b) Is the event she passes one course independent of the event that she passes the other course?

Two events are independent when P(A∩B) = P(A) * P(B)

So far, we don't know P(A∩B), but we do know that for all events, the next formula is true:

P(A∪B) = P(A) + P(B) - P(A∩B)

We are going to solve for P (A∩B)

.98 = .73 + .66 - P(A∩B)

P(A∩B) =.73 + .66 - .98

P(A∩B) = .41

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P(A∩B) = P(A) x P(B)

.41 = .73 x .66

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Therefore, these two events are not independent.

c) The probability she does not pass either course, is 1 - the probability that she passes either one of the courses (P(A∪B) = .98)

1 - P(A∪B) = 1 - .98 = .02

d) The probability she doesn't pass both courses is 1 - the probability that she passes both of the courses P(A∩B)

1 - P(A∩B) = 1 -.41 = .59

e) The probability she passes exactly one course would be the probability that she passes either course minus the probability that she passes both courses.

P(A∪B) - P(A∩B) = .98 - .41 = .57

f) Given that she passes the first course, the probability she passes the second would be a conditional probability P(B|A)

P(B|A) = P(A∩B) / P(A)

P(B|A) = .41 / .73 = .5616

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