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pashok25 [27]
2 years ago
6

Find the equation of the straight line that passes through the points (1, 10) and (3, 2)

Mathematics
2 answers:
slava [35]2 years ago
8 0

Answer:

y = -4x+14

Step-by-step explanation:

First find the slope

m = (y2-y1)/(x2-x1)

m = (2-10)/(3-1)

  =-8/2

  = -4

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = -4x+b

Substitute a point into the equation

10 = -4(1)+b

Add 4 to each side

14 = b

y = -4x+14

mylen [45]2 years ago
5 0

Answer:

y=-4x+14

Step-by-step explanation:

m=y1-y2/(x1-x2) and m= y-y1/x-x1

10-2/1-3=-4

m=-4     so          -4=y-10/x-1

                           -4x+4=y-10

                            -4x+14=y

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Step-by-step explanation:

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name a transformation that does not always produce an image that would be congruent to the original figure
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A dilation is the best answer. A dilation shrinks or expands the shape on a plane. But now, that shape is the same shape, but a different size.
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3 years ago
Select all of the following that are quadratic equations.
Lelechka [254]

Answer:

3x ^2 + 5x - 7 = 0

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6 0
2 years ago
-
alisha [4.7K]

Answer:

d=3\sqrt{2}\ units

Step-by-step explanation:

<u><em>The complete question is</em></u>

Line L contains points (3, 5) and (7, 9). Points P has coordinates (2, 10). Find the distance from P to L

step 1

Find the equation of the line L contains points (3,5) and (7,9)

<em>Find the slope</em>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the given values

m=\frac{9-5}{7-3}

m=\frac{4}{4}=1

<em>Find the equation of the line in point slope form</em>

y-y1=m(x-x1)

we have

m=1\\point\ (3,5)

substitute

y-5=(1)(x-3)

isolate the variable y

y=x-3+5

y=x+2 -----> equation A

step 2

Find the equation of the perpendicular line to the given line L  that passes through the point P

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal

so

The slope of the given line L  is m=1

The slope of the line perpendicular to the given line L  is

m=-1

<em>Find the equation of the line in point slope form</em>

y-y1=m(x-x1)

we have

m=-1\\point\ (2,10)

substitute

y-10=-(x-2)

isolate the variable y

y=-x+2+10

y=-x+12 ----> equation B

step 3

Find the intersection point equation A and equation B

y=x+2 -----> equation A

y=-x+12 ----> equation B

solve the system by graphing

The intersection point is (5.7)

see the attached figure

step 4

we know that

The distance from point P to the the line L is equal to the distance between the point P and point (5,7)

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

we have

(2,10) and (5,7)

substitute

d=\sqrt{(7-10)^{2}+(5-2)^{2}}

d=\sqrt{(-3)^{2}+(3)^{2}}

d=\sqrt{18}\ units

simplify

d=3\sqrt{2}\ units

see the attached figure to better understand the problem

6 0
3 years ago
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