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Quiz 3-3 Parallel and Perpendicular Lines on the Coordinate Plane (Gina Wilson All Things Algebra 2014-2019) need these for a quiz please!

Quiz 3-3 Parallel and Perpendicular Lines on the Coordinate Plane (Gina Wilson All Things Algebra 2

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Answer from: nyandog50

14. y = -2x -1

15. $y = -\frac{3}{4}x +3$

16. y= 4x + 9

17. $y = -\frac{5}{3}x -2$

18. $y= -\frac{2}{3}x -5$

19. y = 4x -3

20. y = -3x -7

Step-by-step explanation:

Solving (14):

Given

(x_1,y_1) = (-7,13)

Slope (m) = -2

Equation in slope- intercept form is:

y - y_1 = m(x-x_1)

Substitute values for y1, m and x1

y - 13 = -2(x -(-7))

y - 13 = -2(x +7)

y - 13 = -2x -14

Collect Like Terms

y = -2x -14 + 13

y = -2x -1

Solving (15):

Given

(x_1,y_1) = (-4,6)

$Slope (m) = -\frac{3}{4}$

Equation in slope- intercept form is:

y - y_1 = m(x-x_1)

Substitute values for y1, m and x1

$y - 6 = -\frac{3}{4}(x - (-4))$

$y - 6 = -\frac{3}{4}(x +4)$

$y - 6 = -\frac{3}{4}x -3$

Collect Like Terms

$y = -\frac{3}{4}x -3 + 6$

$y = -\frac{3}{4}x +3$

Solving (16):

Given

(x_1,y_1) = (-5,-11)

(x_2,y_2) = (-2,1)

First, we need to calculate the $slope\ (m)$

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

$m = \frac{1 - (-11)}{-2 - (-5)}$

$m = \frac{1 +11}{-2 +5}$

$m = \frac{12}{3}$

m = 4

Equation in slope- intercept form is:

y - y_1 = m(x-x_1)

Substitute values for y1, m and x1

y - (-11) = 4(x -(-5))

y +11 = 4(x+5)

y +11 = 4x+20

Collect Like Terms

y= 4x + 20 - 11

y= 4x + 9

Solving (17):

Given

(x_1,y_1) = (-6,8)

(x_2,y_2) = (3,-7)

First, we need to calculate the $slope\ (m)$

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

$m = \frac{-7 - 8}{3- (-6)}$

$m = \frac{-7 - 8}{3+6}$

$m = \frac{-15}{9}$

$m = -\frac{5}{3}$

Equation in slope- intercept form is:

y - y_1 = m(x-x_1)

Substitute values for y1, m and x1

$y - 8 = -\frac{5}{3}(x -(-6))$

$y - 8 = -\frac{5}{3}(x +6)$

$y - 8 = -\frac{5}{3}x -10$

Collect Like Terms

$y = -\frac{5}{3}x -10 + 8$

$y = -\frac{5}{3}x -2$

18.

Given

(x_1,y_1) = (-6,-1)

$y = -\frac{2}{3}x+1$

Since the given point is parallel to the line equation, then the slope of the point is calculated as:

m_1 = m_2

Where m_2 represents the slope

Going by the format of an equation, y = mx + b ; by comparison

$m = -\frac{2}{3}$

and

$m_1 = m_2 = -\frac{2}{3}$

Equation in $slope\ intercept\ form$ is:

y - y_1 = m(x-x_1)

Substitute values for y1, m and x1

$y - (-1) = -\frac{2}{3}(x - (-6))$

$y +1 = -\frac{2}{3}(x +6)$

$y +1 = -\frac{2}{3}x -4$

$y= -\frac{2}{3}x -4 - 1$

$y= -\frac{2}{3}x -5$

19.

Given

(x_1,y_1) = (-2,-11)

$y = -\frac{1}{4}x+2$

Since the given point is parallel to the line equation, then the slope of the point is calculated as:

$m_1 = -\frac{1}{m_2}$

Where m_2 represents the slope

Going by the format of an equation, y = mx + b ; by comparison

$m_2 = -\frac{1}{4}$

and

$m_1 = -\frac{1}{m_2}$

$m_1 = -1/\frac{-1}{4}$

$m_1 = -1*\frac{-4}{1}$

m_1 = 4

Equation in $slope\ intercept\ form$ is:

y - y_1 = m(x-x_1)

(x_1,y_1) = (-2,-11)

Substitute values for y1, m and x1

y - (-11) = 4(x - (-2))

y +11 = 4(x +2)

y +11 = 4x +8

Collect Like Terms

y = 4x + 8 - 11

y = 4x -3

20.

Given

(x_1,y_1) = (-10,3)

(x_2,y_2) = (2,7)

First, we need to calculate the slope of the given points

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

$m = \frac{7 - 3}{2 - (-10)}$

$m = \frac{7 - 3}{2 +10}$

$m = \frac{4}{12}$

$m = \frac{1}{3}$

Next, we determine the slope of the perpendicular bisector using:

$m_1 = -\frac{1}{m_2}$

$m_1 = -1/\frac{1}{3}$

m_1 = -3

Next, is to determine the coordinates of the bisector.

To bisect means to divide into equal parts.

So the coordinates of the bisector is the midpoint of the given points;

$Midpoint = [\frac{1}{2}(x_1+x_2),\frac{1}{2}(y_1+y_2)]$

$Midpoint = [\frac{1}{2}(-10+2),\frac{1}{2}(3+7)]$

$Midpoint = [\frac{1}{2}(-8),\frac{1}{2}(10)]$

Midpoint = (-4,5)

So, the coordinates of the midpoint is:

(x_1,y_1) = (-4,5)

Equation in slope- intercept form is:

y - y_1 = m(x-x_1)

Substitute values for y1, m and x1: m_1 = -3 & (x_1,y_1) = (-4,5)

y - 5 = -3(x - (-4))

y - 5 = -3(x +4)

y - 5 = -3x-12

Collect Like Terms

y = -3x - 12 +5

y = -3x -7

Answer from: Quest

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

Answer from: Quest

answer: integers are just whole numbers: positive, negative, and zero.

i = {-∞, -2, -1, 0, 1, 2, 3, ∞}

let x = 1st integer

let y = 2nd integer

x = 3y + 17 {equation 1}

xy = -24 {equation 2}

substitute 3y+17 in place of x n equation 2

and solve for y.

(3y+17)y = -24

3y2 + 17y = -24

3y2 + 17y + 24 = 0

from quadratic equation:

y = [-17±√(172-4(3)(24))]/(2(3))

y = (-17 ±√1)/6

y = (-17+1)/6 or y = (-17-1)/6

y = -16/6 or y = -18/6

y = -2 2/3 or y = -3

since we are dealing with

y = -3

x = 3y+17 = -9+17 = 8

the integers are -3, 8

step-by-step explanation:

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Quiz 3-3 Parallel and Perpendicular Lines on the Coordinate Plane (Gina Wilson All Things Algebra 20...

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