Question

Match each pair of points to the equation of the line that is parallel to the line passing through the points.

Answer 1

we know that

If two lines are parallel, then, their slopes are equal.

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

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

we will proceed to calculate the slope in each case, to determine the solution of the problem

Case A) Point $B(5,2)\ C(7,-5)$

Find the slope BC

Substitute the values in the formula

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

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

$m=-3.5$

so

The equation $y=-3.5x-15$ is parallel to the line passing through the points $B(5,2)\ C(7,-5)$

therefore

the answer Part A) is

$B(5,2)\ C(7,-5)$ ------> $y=-3.5x-15$

Case B) Point $D(11,6)\ E(5,9)$

Find the slope DE

Substitute the values in the formula

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

$m=\frac{3}{-6}$

$m=-0.5$

so

The equation $y=-0.5x-3$ is parallel to the line passing through the points $D(11,6)\ E(5,9)$

therefore

the answer Part B) is

$D(11,6)\ E(5,9)$ ------> $y=-0.5x-3$

Case C) Point $F(-7,12)\ G(3,-8)$

Find the slope FG

Substitute the values in the formula

$m=\frac{-8-12}{3+7}$  

$m=\frac{-20}{10}$

$m=-2$

so

Any linear equation with slope $m=-2$ will be parallel to the line passing through the points $F(-7,12)\ G(3,-8)$

Case D) Point $H(4,4)\ I(8,9)$

Find the slope HI

Substitute the values in the formula

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

$m=\frac{5}{4}$

$m=1.25$

so

The equation $y=1.25x+4$ is parallel to the line passing through the points $H(4,4)\ I(8,9)$

therefore

the answer Part D) is

$H(4,4)\ I(8,9)$ ------> $y=1.25x+4$

Case E) Point $J(7,2)\ K(-9,8)$

Find the slope JK

Substitute the values in the formula

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

$m=\frac{6}{-16}$

$m=-0.375$

so

Any linear equation with slope $m=-0.375$ will be parallel to the line passing through the points  $J(7,2)\ K(-9,8)$

Case F) Point $L(5,-7)\ M(4,-12)$

Find the slope LM

Substitute the values in the formula

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

$m=\frac{-5}{-1}$

$m=5$

so

The equation $y=5x+19$ is parallel to the line passing through the points $L(5,-7)\ M(4,-12)$

therefore

the answer Part F) is

$L(5,-7)\ M(4,-12)$ ------>  $y=5x+19$

Answer 2

Answer:

Step-by-step explanation:

Plato Answer simplified:

(4,4) (8,9) - y=1.25x+4

(5,2) (7,-5) - y=-3.5x-15

(11,6) (5,9) - y=-0.5x-3

(5,-7) (4,-12) - y=5x+19

Example of how to do it in your head if you have multiple choice:

Note the order, you start from right to left with the coordinates...

(4,4) (8,9) - y=1.25x+4

9   -    4     The Y's         5

8   -    4     The X's         4

                                      _

                                    1.25x

(5,2) (7,-5) - y=-3.5x-15

-5   -    2     The Y's        -7

7   -    5     The X's         2

                                       _

                                    -3.5x

(11,6) (5,9) - y=-0.5x-3

9   -    6     The Y's         3

5   -    11     The X's        -6

                                       _

                                    -0.5x

(5,-7) (4,-12) - y=5x+19

-12   -    -7     The Y's        -5

 4   -     5     The X's         -1

                                         _

                                         5x