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

$m=\frac{y_2-y_1}{x_2-x_1}$

we can plug values

$m=\frac{-5-2}{7-5}$

$m=-3.5$

we can use point slope form of line

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

we can plug values

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

$y=\frac{-7}{2}x+\frac{39}{2}$...........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

$m=\frac{y_2-y_1}{x_2-x_1}$

we can plug values

$m=\frac{9-6}{5-11}$

$m=-0.5$

we can use point slope form of line

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

we can plug values

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

$y=\frac{-1}{2}x+\frac{23}{2}$...........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

$m=\frac{y_2-y_1}{x_2-x_1}$

we can plug values

$m=\frac{-8-12}{3+7}$

$m=-2$

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

$m=\frac{y_2-y_1}{x_2-x_1}$

we can plug values

$m=\frac{9-4}{8-4}$

$m=1.25$

we can use point slope form of line

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

we can plug values

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

$y=\frac{5}{4}x-1$...........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

$m=\frac{y_2-y_1}{x_2-x_1}$

we can plug values

$m=\frac{8-2}{-9-7}$

$m=-\frac{3}{8}$

we can use point slope form of line

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

we can plug values

$y-2=\frac{3}{8}(x-7)$

$y=\frac{3}{8}x-\frac{5}{8}$...........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

$m=\frac{y_2-y_1}{x_2-x_1}$

we can plug values

$m=\frac{-12+7}{4-5}$

$m=5$

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:

        $\frac{y-b}{x-a}=\frac{b-d}{a-c}$

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

    $\rightarrow \frac{y-2}{x-5}=\frac{-5-2}{7-5}\\\\\rightarrow \frac{y-2}{x-5}=\frac{-7}{2}\\\\\rightarrow2y-4= -7x+35\\\\\rightarrow 2 y=-7 x +39\\\\\rightarrow y=\frac{-7x}{2}+\frac{39}{2}$

If two lines are parallel then their slopes are equal.

Any line have ,slope equal to,$\frac{-7}{2}= -3.5$ 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:

        $\rightarrow\frac{y-6}{x-11}=\frac{9-6}{5-11}\\\\\rightarrow\frac{y-6}{x-11}=\frac{3}{-6}\\\\\rightarrow\frac{y-6}{x-11}=\frac{1}{-2}\\\\\rightarrow-2 y+12=x-11\\\\\rightarrow -2 y=x-23\\\\\rightarrow y=\frac{-x}{2}+\frac{23}{2}$

 If two lines are parallel then their slopes are equal.

  Any line have ,slope equal to,$\frac{-1}{2}= -0.5$ 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:

        $\rightarrow\frac{y-12}{x+7}=\frac{12+8}{-7-3}\\\\\rightarrow\frac{y-12}{x+7}=\frac{20}{-10}\\\\\rightarrow\frac{y-12}{x+7}=-2\\\\\rightarrow y-12=-2 x-14\\\\\rightarrow y=-2 x-2$

 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:

        $\rightarrow\frac{y-4}{x-4}=\frac{9-4}{8-4}\\\\\rightarrow\frac{y-4}{x-4}=\frac{5}{4}\\\\\rightarrow 4 y-16=5 x-20\\\\\rightarrow 4 y=5 x-4\\\\\rightarrow y=\frac{5 x}{4}-1$

 If two lines are parallel then their slopes are equal.

  Any line have ,slope equal to $\frac{5}{4}= 1.25$,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:

        $\rightarrow\frac{y-2}{x-7}=\frac{8-2}{-9-7}\\\\\rightarrow\frac{y-2}{x-7}=\frac{6}{-16}\\\\\rightarrow -16 y+32=6x-42\\\\\rightarrow-16 y=6 x-74\\\\\rightarrow y=\frac{6x}{-16}+\frac{74}{16}\\\\\rightarrow y=\frac{-3x}{8}+\frac{37}{8}$

 If two lines are parallel then their slopes are equal.

  Any line have ,slope equal to $\frac{-3}{8}= -0.375$,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:

        $\rightarrow\frac{y+7}{x-5}=\frac{-12+7}{4-5}\\\\\rightarrow\frac{y+7}{x-5}=\frac{-5}{-1}\\\\\rightarrow 5 x-25=y+7\\\\\rightarrow y=5 x-32$

 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