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trapecia [35]
2 years ago
14

The equation of the line that is parallel to 4x+2 and passing through (5,15)

Mathematics
1 answer:
Mila [183]2 years ago
8 0

Answer:

y=4x-5.

Step-by-step explanation:

slop-interception form of the required line is y=kx+b, where k - slop, b - intercept;

1) to find value of k:

if the required line is parallel to the given line, then slop of the given line = slop of the required line, it means k=4 and the required line is y=4x+b;

2) to find the value of 'b':

if to substitute the given coordinates into the equation of the given line, then:

15=4*5+b, b= -5.

3) finally, y=4x-5

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Find the sum 3 + (-6)
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Next, we must just perform the subtraction.

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Therefore, your answer is -3.

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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

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