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Kisachek [45]
3 years ago
14

Write the point-slope equation of the line that passes through(3,5) and (7,1)

Mathematics
1 answer:
Liono4ka [1.6K]3 years ago
5 0

Answer:   y - 1 = –(x –7)

or   y –5 = –1(x –3)

The attachment shows the graph of these equations (identical)

Step-by-step explanation:

The basic form for a point-slope equation is

y - b = m(x - a)

a is the x-value from the given coordinate,  b is the y-value form the given coordinate,  m is the slope. x and y are the variables in the function.

To find the slope, m, use the given coordinates. Get the difference in the y-values and divide by the difference in the x-values. This is "rise over run."

Subtract the first coordinate from the second coordinate.

Given coordinate points: ​(3​,5) and ​(7​,1)    substitute values:

m= 1 –5 / 7 –3  becomes  m= –4/4   so the slope, m = –4/4

That is –1  The "1" is "understood," so only the negative sign represents the slope  in the equation

To write the equation:  Take the basic form, substitute b and a values from either given coordinate. And use the value of m we just calculated.

y - b = m(x - a)  Using the second coordinate: (7,1)

y - 1 = –(x –7)

or using the first coordinate:

y –5 = –(x –3)

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The circle described by the equation <img src="https://tex.z-dn.net/?f=%28x-3%29%5E%7B2%7D%20%2B%28y%2B4%29%5E%7B2%7D%3D9" id="T
ElenaW [278]

Answer:

The point at which center of the image circle located is (-2, -3) so second option is correct.

Step-by-step explanation:

Given equation of circle is:

(x-3)^{2} + (y+4)^{2} = 9 (i)

The general equation of circle is mentioned below,

(x-h)^{2} + (y-k)^{2} = r^{2} (ii)

Here 'r' represents the radius of the circle and (h,k) shown the center of the circle.

By comparing equation (i) and equation (ii), we get

r^2 = 9

r = 3

(x-3)^{2} = (x-h)^{2}

(x-3) = (x-h)

h = 3

(y+4)^{2} = (y-k)^{2}

(y+4) = (y-k)

k = -4

So the center of given circle is (h,k) = (3,-4)

Also, the circle is translated 5 units left, that is towards the -x-axis. Therefore h = 3 - 5 = -2

Also, the circle is translated 1 unit up, that is towards the +y-axis. Therefore k = -4 + 1 = -3

Hence, the point at which center of the image circle located is (-2, -3) so second option is correct.

6 0
3 years ago
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    + 4 + 4
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4 0
3 years ago
Sam received 74 dollars for his birthday. He went to a sporting goods store and bought a baseball glove, baseball,and bat. He ha
tigry1 [53]

Answer:

he spent 48 dollars

Step-by-step explanation:

74-x=26

or

74-26=x

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3 years ago
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Answer:

0.12 miles is it flying per second.

Step-by-step explanation:

The distance d is related to time t in seconds is given by the equation as follows :

d =0.12 t

We need to find how many miles is it flying per second.

\dfrac{d}{t}=0.12\\\\\dfrac{\text{miles}}{\text{second}}=0.12

So, the speed of the airplane is 0.12 miles per second, Hence, 0.12 miles is it flying per second.

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