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Alex73 [517]
2 years ago
14

What is an equation of the line that passes through the points (-6, -2) and

Mathematics
1 answer:
den301095 [7]2 years ago
6 0

Answer:

The equation of line is: \mathbf{4x-3y=-18}

Step-by-step explanation:

We need to find an equation of the line that passes through the points (-6, -2) and  (-3, 2)?

The equation of line in slope-intercept form is: y=mx+b

where m is slope and b is y-intercept.

We need to find slope and y-intercept.

Finding Slope

Slope can be found using formula: Slope=\frac{y_2-y_1}{x_2-x_1}

We have x_1=-6,y_1=-2, x_2=-3, y_2=2

Putting values and finding slope

Slope=\frac{2-(-2)}{-3-(-6)}\\Slope=\frac{2+2}{-3+6} \\Slope=\frac{4}{3}

So, we get slope: m=\frac{4}{3}

Finding y-intercept

Using point (-6,-2) and slope m=\frac{4}{3} we can find y-intercept

y=mx+b\\-2=\frac{4}{3}(-6)+b\\-2=4(-2)+b\\-2=-8+b\\b=-2+8\\b=6

So, we get y-intercept b= 6

Equation of required line

The equation of required line having slope m=\frac{4}{3} and y-intercept b = 6 is

y=mx+b\\y=\frac{4}{3}x+6

Now transforming in fully reduced form:

y=\frac{4x+6*3}{3} \\y=\frac{4x+18}{3} \\3y=4x+18\\4x-3y=-18

So, the equation of line is: \mathbf{4x-3y=-18}

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* brackets means multiplying

Final answer is 108
8 0
3 years ago
An electrician must use 15 miles of electrical cable between electric poles. How many yards of cable will be used?
Dmitry [639]

Answer:

The 3rd option or 39,600 would be the correct answer.

Step-by-step explanation:

Hope this helps:)

7 0
2 years ago
An urn contains 12 balls, of which 4 are white.
wel

Answer:

a) \frac{1}{3}

b) \frac{4}{12}\,,\,\frac{4}{11}\,,\,\frac{4}{10}\,,...

Step-by-step explanation:

Number of balls in the urn = 12

Number of white balls in the urn = 4

So, number of balls which are not white = 12 - 4 = 8

We know that probability = No. of outcomes/Total number of outcomes

Let A_i\,,\,B_i\,,\,C_i denotes the event of getting white ball by A, B and C

a) each ball is replaced after being drawn.

Probability = Number of white balls/Total number of balls

Solution: P(A_i)=P(B_i)=P(C_i)=\frac{4}{12}=\frac{1}{3}

b)the balls that are withdrawn are not replaced.

Solution:

If A wins: P(A_1)=\frac{4}{12}=\frac{1}{3}

If A lost and B wins: P\left ( B_1|A_1^{c} \right )=\frac{4}{11}

If A and B lost and C wins: P\left ( C_1|A_1^{c}\,B_1^{c} \right )=\frac{4}{10}

and so on....

4 0
3 years ago
For which intervals is the function decreasing?
lilavasa [31]

Answer:

The function is decreasing in the following intervals

A. (0, 1)

C. (2, pi)

Step-by-step explanation:

To answer this question, imagine that you draw lines of slope m parallel to the function shown at each point.

-If the slope of this line parallel to the function is negative for those points then the function is decreasing.

-If the slope of this line parallel to the function is positive for those points then the function is increasing.

Observe in the lines drawn in the attached image. You can see that they have slope less than zero in the following interval:

(0, 1) U (2, pi)

Therefore the correct option is:

A. (0, 1)

C. (2, pi)

5 0
3 years ago
Given: F(x) = 2x + 3, find F(X+h)-f(x) and simplify.<br> 01<br> 02<br> (2h+6)/h
antiseptic1488 [7]
F(x+h) = 2(x+h) +3= 2x + 2h +3
f(x) = 2x + 5

f(x+h) - f(x) = 2x + 2h + 3- 2x - 3= 2h

[f(x+h) - f(x)]/h = 2h/h = 2

6 0
3 years ago
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