Mathematics, 09.07.2019 22:00, bubl6010

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)

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answered: andrewbigbrains8740

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:

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