All categories

3 years ago

What is the equation of a line, in general form, that passes through point (1,-2) and has a siope of 1/3?

Mathematics

1 answer:

Sever21 [200]3 years ago

8 0

9514 1404 393

Answer:

x -3y -7 = 0

Step-by-step explanation:

The general form of the equation for a line is ...

ax +by +c = 0

where a, b, c are mutually prime and the leading coefficient is greater than zero.

The general form equation for a line with slope m = rise/run through point (h, k) can be found by simplifying ...

rise(x -h) -run(y -k) = 0 . . . . where run has the sign of the slope

For the given point and slope, we have ...

1(x -1) -3(y -(-2)) = 0

x -3y -7 = 0

You might be interested in

What is the equation of the line that passes through the point (4, 3) and is perpendicular to the line x + y = 4?

zimovet [89]

ANSWER

$y - x = - 1$

EXPLANATION

The required equation passes through:

(4,3) and is perpendicular to x+y=4.

Rewrite the given equation in slope-intercept form:

$y = - x + 4$

The slope of this line is -1.

The slope of the required line is perpendicular to this line, so we find the negative reciprocal of this slope.

$m= - \frac{1}{ - 1} = 1$

The equation of the line can be found using:

$y - y_1 = m(x - x_1)$

We substitute the slope and point to obtain:

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

We simplify to get:

$y - 3 = x - 4$

$y - x = - 4 + 3$

The required equation is

$y - x = - 1$

5 0

3 years ago

Twenty percent of drivers driving between 10 pm and 3 am are drunken drivers. In a random sample of 12 drivers driving between 1

Lesechka [4]

Answer:

(a) 0.28347

(b) 0.36909

(d) 0.9806

Step-by-step explanation:

Given information:

n=12

p = 20% = 0.2

q = 1-p = 1-0.2 = 0.8

Binomial formula:

$P(x=r)=^nC_rp^rq^{n-r}$

(a) Exactly two will be drunken drivers.

$P(x=2)=^{12}C_{2}(0.2)^{2}(0.8)^{12-2}$

$P(x=2)=66(0.2)^{2}(0.8)^{10}$

$P(x=2)=\approx 0.28347$

Therefore, the probability that exactly two will be drunken drivers is 0.28347.

(b)Three or four will be drunken drivers.

$P(x=3\text{ or }x=4)=P(x=3)\cup P(x=4)$

$P(x=3\text{ or }x=4)=P(x=3)+P(x=4)$

Using binomial we get

$P(x=3\text{ or }x=4)=^{12}C_{3}(0.2)^{3}(0.8)^{12-3}+^{12}C_{4}(0.2)^{4}(0.8)^{12-4}$

$P(x=3\text{ or }x=4)=0.236223+0.132876$

$P(x=3\text{ or }x=4)\approx 0.369099$

Therefore, the probability that three or four will be drunken drivers is 0.3691.

(c)

At least 7 will be drunken drivers.

$P(x\geq 7)=1-P(x$

$P(x\leq 7)=1-[P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)+P(x=6)]$

$P(x\leq 7)=1-[0.06872+0.20616+0.28347+0.23622+0.13288+0.05315+0.0155]$

$P(x\leq 7)=1-[0.9961]$

$P(x\leq 7)=0.0039$

Therefore, the probability of at least 7 will be drunken drivers is 0.0039.

(d) At most 5 will be drunken drivers.

$P(x\leq 5)=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)$

$P(x\leq 5)=0.06872+0.20616+0.28347+0.23622+0.13288+0.05315$

$P(x\leq 5)=0.9806$

Therefore, the probability of at most 5 will be drunken drivers is 0.9806.

5 0

3 years ago

How do you say 876543 in word form

Valentin [98]

Eight hundred seventy six thousand five hundred forty three.

7 0

3 years ago

Read 2 more answers

jonathan is traveling from new york city to wellington, new zealand. thr latitude of new york city is 40.67°, and the latitude o

Cloud [144]

Well a difference is the difference between them. difference means subtraction. So so a difference can be written as:
40.67 - (-41.29)

If you subtract a negative number you really add it. to make sense of this you could say 40.67 is 40.67 units away from zero in the positive direction. whereas -41.29 is 41.29 units away in the negative direction. since they go in opposite directions away from zero that means that thw length between them is extended and must then be added together. So
40.67 + 41.29 = 81.96

3 0

3 years ago

Read 2 more answers

Identify the constant of<br> proportionality (k)<br> 8Y = 16x<br> k=

RUDIKE [14]

Answer:

JUST WRITE THIS AS YOUR ANSWER

Step-by-step explanation:

Step 1: Put together the general equation.

Step 2: Solve for the constant of proportionality.

Step 3: Plugging the constant into the equation, solve for the unknown variable.

Let's solve a few problems to see how this works, shall we?

Example 1: Y is directly proportional to x. When x = 5, y = 8. What does y equal when x = 9?

First, we set up our general equation. Because y is directly proportional to x, we have:

y = cx

where c is the constant of proportionality. In other words, when x goes up, y goes up, and when x goes down, y goes down.

The next thing we do is plug our values for x and y into the equation so we can solve for c:

8 = (c)(5)

Solving for c, we get c = 8/5 = 1.6 and we plug this into our equation:

y = 1.6x

Now, we can plug x = 9 into the equation to find out what y equals:

y = (1.6)(9)

y = 14.4

So, our answer is 14.4

Example 2: Y is directly proportional to the square of x. When x = 2, y = 32. What does y equal when x = 5?

This time, our general equation is slightly more complicated because x is squared:

y = cx2

Like before, we solve for our constant:

32 = (c)(22)

32 = (c)(4)

We get c = 8:

y = 8x2

Solving for y when x = 5, we get y = (8)(52) = (8)(25) = 200

Example 3: Y is inversely proportional to x. When x = 2, y = 8. What does y equal when x = 24?

This time, because y is inversely proportional to x, our general equation is different:

xy = c

so when x goes up, y goes down, and vise versa. But, other than that, we solve these kinds of problems the same way as direct proportion problems. Solving for the constant, we get:

(2)(8) = c

So c = 16 and our equation is now:

xy = 16

Solving for y when x = 24 we get y = 16/24 = 2/3

Example 4: Y is inversely proportional to the square root of x. When x = 36, y = 2. What does y equal when x = 64?

As before, we set up our equation:

eq001

Since the square root of 36 is 6, it is easy to solve for c:

(6)(2) = c

We get c = 12 and our equation is now:

eq002

Solving for y when x = 64 we get 8y = 12 or y = 12/8 = 1.5 because the square root of 64 is 8.

6 0

2 years ago