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1 year ago

Write the equation of the line that passes through the points (-6,-1) and (-4,2). Put your answer in fully simplified point-slop

e form, unless it is a vertical or horizontal line.

Mathematics

1 answer:

Archy [21]1 year ago

4 0

$(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-6)}}} \implies \cfrac{2 +1}{-4 +6} \implies \cfrac{ 3 }{ 2 }$

$\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{\cfrac{3}{2}}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y +1= \cfrac{3}{2} (x +6) \end{array}}$

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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seraphim [82]

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$\frac{1}{8}$

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3 years ago

Please help! question attached

Svetradugi [14.3K]

Answer:

36. y=x

37. x=4

38. y=3x-10

39. y=-25x+49

40. $y=-\dfrac{1}{18}x-\dfrac{89}{18}$

41. y=-x+3

Step-by-step explanation:

36. Parallel lines have the same slope. The slope of the line $y=x+42$ is $m=1,$ so the equation of a parallel line is

$y=x+b$

This line passes through the point (2,2), so its coordinates satisfy the equation:

$2=2+b\\ \\b=0$

and the equation of the line is $y=x$

37. The line $x=03$ is vertical ine, so parallel line is also vertical line with equation $x=a.$ Substitute the coordinates of the point (4,3):

$4=a$

hence the equation is $x=4$

38. Parallel lines have the same slope. The slope of the line $y=3x+24$ is $m=3,$ so the equation of a parallel line is

$y=3x+b$

This line passes through the point (2,-4), so its coordinates satisfy the equation:

$-4=3\cdot 2+b\\ \\b=-10$

and the equation of the line is $y=3x-10$

39. Parallel lines have the same slope. The slope of the line $y=-25x+35$ is $m=-25,$ so the equation of a parallel line is

$y=-25x+b$

This line passes through the point (2,-1), so its coordinates satisfy the equation:

$-1=-25\cdot 2+b\\ \\b=49$

and the equation of the line is $y=-25x+49$

40. Perpendicular lines have slopes satisfying $m_1\cdot m_2=-1$ Since the line $y=18x+26$ has the slope $m_1=18,$ perpendicular line has the slope $m_2 =-\dfrac{1}{18}.$

The equation is

$y=-\dfrac{1}{18}x+b$

This line passes through the point (1,-5), so its coordinates satisfy the equation:

$-5=-\dfrac{1}{18}\cdot 1+b\\ \\b=-5+\dfrac{1}{18}=-\dfrac{89}{18}$

and the equation of the line is $y=-\dfrac{1}{18}x-\dfrac{89}{18}$

41. Perpendicular lines have slopes satisfying $m_1\cdot m_2=-1$ Since the line $y=x+2$ has the slope $m_1=1,$ perpendicular line has the slope $m_2 =-1.$