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3 years ago

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If 9 = c, then c = 9. What algebraic equality property justifies the above statement?

1 answer:

netineya [11]3 years ago

4 0

Symmetric property is the correct term

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Step-by-step explanation:

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Answer:

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

$y = -3x - 12 +5$

$y = -3x -7$

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