Question

Match each pair of points to the equation of the line that is parallel to the line passing through the pointsB(5,2) and C(7,-5)Y=(-0.5x-3) D(11,6) and E(5,9)Y=(-3.5x-15)F(-7,12) and G(3,-8)Y=5x+19H(4,4) and I(8,9)Y=1.25x+4J(7,2) and K(-9,8)L(5,-7) and M(4,-12)

Answer 1

we will select each points and find equation of line

option-A:

points are B(5,2) and C(7,-5)

x1=5,y1=2 , x2=7 , y2=-5

Firstly, we will find slope

`m=(y_2-y_1)/(x_2-x_1)`

we can plug values

`m=(-5-2)/(7-5)`

`m=-3.5`

we can use point slope form of line

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

we can plug values

`y-2=-3.5(x-5)`

`y=(-7)/(2)x+(39)/(2)`...........Answer

option-B:

points are D(11,6) and E(5,9)

x1=11,y1=6 , x2=5 , y2=9

Firstly, we will find slope

`m=(y_2-y_1)/(x_2-x_1)`

we can plug values

`m=(9-6)/(5-11)`

`m=-0.5`

we can use point slope form of line

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

we can plug values

`y-6=-0.5(x-11)`

`y=(-1)/(2)x+(23)/(2)`...........Answer

option-C:

points are F(-7,12) and G(3,-8)

x1=-7,y1=12 , x2=3 , y2=-8

Firstly, we will find slope

`m=(y_2-y_1)/(x_2-x_1)`

we can plug values

`m=(-8-12)/(3+7)`

`m=-2`

we can use point slope form of line

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

we can plug values

`y-12=-2(x+7)`

`y=-2x-2`...........Answer

option-D:

points are H(4,4) and I(8,9)

x1=4,y1=4 , x2=8 , y2=9

Firstly, we will find slope

`m=(y_2-y_1)/(x_2-x_1)`

we can plug values

`m=(9-4)/(8-4)`

`m=1.25`

we can use point slope form of line

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

we can plug values

`y-4=1.25(x-4)`

`y=(5)/(4)x-1`...........Answer

option-E:

points are J(7,2) and K(-9,8)

x1=7,y1=2 , x2=-9 , y2=8

Firstly, we will find slope

`m=(y_2-y_1)/(x_2-x_1)`

we can plug values

`m=(8-2)/(-9-7)`

`m=-(3)/(8)`

we can use point slope form of line

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

we can plug values

`y-2=(3)/(8)(x-7)`

`y=(3)/(8)x-(5)/(8)`...........Answer

option-F:

points are L(5,-7) and M(4,-12)

x1=5,y1=-7 , x2=4 , y2=-12

Firstly, we will find slope

`m=(y_2-y_1)/(x_2-x_1)`

we can plug values

`m=(-12+7)/(4-5)`

`m=5`

we can use point slope form of line

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

we can plug values

`y+7=5(x-5)`

`y=5x-32`...........Answer

Answer 2

Answer with explanation:

Equation of line passing through two points (a,b) and (c,d) is given by:

`(y-b)/(x-a)=(b-d)/(a-c)`

1.⇒Equation of line passing through , B(5,2) and C (7,-5) is given by:

`\rightarrow (y-2)/(x-5)=(-5-2)/(7-5)\\\\\rightarrow (y-2)/(x-5)=(-7)/(2)\\\\\rightarrow2y-4= -7x+35\\\\\rightarrow 2 y=-7 x +39\\\\\rightarrow y=(-7x)/(2)+(39)/(2)`

If two lines are parallel then their slopes are equal.

Any line have ,slope equal to,
`(-7)/(2)= -3.5` will be parallel to above line.

So, Equation of line Parallel to Above line is:

y= -3.5 x -15

2. ⇒Equation of line passing through , D(11,6) and E (5,9) is given by:

`\rightarrow(y-6)/(x-11)=(9-6)/(5-11)\\\\\rightarrow(y-6)/(x-11)=(3)/(-6)\\\\\rightarrow(y-6)/(x-11)=(1)/(-2)\\\\\rightarrow-2 y+12=x-11\\\\\rightarrow -2 y=x-23\\\\\rightarrow y=(-x)/(2)+(23)/(2)`

If two lines are parallel then their slopes are equal.

Any line have ,slope equal to,
`(-1)/(2)= -0.5` will be parallel to above line.

So, Equation of line Parallel to Above line is:

y= -0.5 x -3

3. ⇒Equation of line passing through , F(-7,12) and G(3,-8) is given by:

`\rightarrow(y-12)/(x+7)=(12+8)/(-7-3)\\\\\rightarrow(y-12)/(x+7)=(20)/(-10)\\\\\rightarrow(y-12)/(x+7)=-2\\\\\rightarrow y-12=-2 x-14\\\\\rightarrow y=-2 x-2`

If two lines are parallel then their slopes are equal.

Any line have ,slope equal to = -2,will be parallel to above line.

So, Equation of line Parallel to Above line is:

..........................................................

4.⇒Equation of line passing through , H(4,4) and I(8,9) is given by:

`\rightarrow(y-4)/(x-4)=(9-4)/(8-4)\\\\\rightarrow(y-4)/(x-4)=(5)/(4)\\\\\rightarrow 4 y-16=5 x-20\\\\\rightarrow 4 y=5 x-4\\\\\rightarrow y=(5 x)/(4)-1`

If two lines are parallel then their slopes are equal.

Any line have ,slope equal to
`(5)/(4)= 1.25`,will be parallel to above line.

So, Equation of line Parallel to Above line is:

y=1.25 x+4

5.⇒Equation of line passing through , J(7,2) and K(-9,8) is given by:

`\rightarrow(y-2)/(x-7)=(8-2)/(-9-7)\\\\\rightarrow(y-2)/(x-7)=(6)/(-16)\\\\\rightarrow -16 y+32=6x-42\\\\\rightarrow-16 y=6 x-74\\\\\rightarrow y=(6x)/(-16)+(74)/(16)\\\\\rightarrow y=(-3x)/(8)+(37)/(8)`

If two lines are parallel then their slopes are equal.

Any line have ,slope equal to
`(-3)/(8)= -0.375`,will be parallel to above line.

So, Equation of line Parallel to Above line is:

...............................................

6. ⇒Equation of line passing through , L(5,-7) and M(4, -12) is given by:

`\rightarrow(y+7)/(x-5)=(-12+7)/(4-5)\\\\\rightarrow(y+7)/(x-5)=(-5)/(-1)\\\\\rightarrow 5 x-25=y+7\\\\\rightarrow y=5 x-32`

If two lines are parallel then their slopes are equal.

Any line have ,slope equal to=5 will be parallel to above line.

So, Equation of line Parallel to Above line is:

y=5 x+19