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22 days ago

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

Mathematics

2 answers:

Svet_ta [9.4K]22 days ago

8 0

It's known that

When two lines are parallel, their slopes are identical.

The slope between any two points can be calculated using the following formula:

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

We will calculate the slope for each case to find the solution to the problem.

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

Determine the slope of BC

Insert the values into the formula:

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

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

$m=-3.5$

Thus,

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

Therefore,

the result for Part A) is

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

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

Calculate the slope of DE

Plug the values into the formula:

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

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

$m=-0.5$

Thus,

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

Therefore,

the result for Part B) is

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

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

Determine the slope of FG

Insert the values into the formula:

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

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

$m=-2$

Thus,

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

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

Calculate the slope of HI

Substitute the values in the formula:

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

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

$m=1.25$

Thus,

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

Therefore,

the result for Part D) is

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

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

Determine the slope of JK

Insert the values into the formula:

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

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

$m=-0.375$

Thus,

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

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

Find the slope of LM

Substitute the values in the formula:

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

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

$m=5$

Thus,

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

Therefore,

the result for Part F) is

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

Svet_ta [9.4K]22 days ago

5 0

Response:

Detailed breakdown of the process:

Summary of Plato’s answer:

(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

A mental method for solving multiple choice questions:

Be mindful of the order; start from right to left with the coordinates...

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

9 - 4 The Y-values 5

8 - 4 The X-values 4

1.25x

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

-5 - 2 The Y-values -7

7 - 5 The X-values 2

-3.5x

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

9 - 6 The Y-values 3

5 - 11 The X-values -6

-0.5x

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

-12 - -7 The Y-values -5

4 - 5 The X-values -1

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