Tell whether the lines through the given points are parallel, perpendicular, or neither.
Line 1: (10,5), (-8, 9)
Line 2: (2, - 4), (11, - 6)
The slope of line 1 is.
The slope of line 2 is.
The two lines are...

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sarengradac sarengradac · Answer 1 · 2020-10-22T00:26:50+02:00

use

[tex]y - y_{1} = \frac{ y_{2} - y_{1}}{x_{2} - x_{1}} \times (x_{2} - x_{1})[/tex]

slope is

[tex]m = \frac{ y_{2} - y_{1}}{x_{2} - x_{1}} \\[/tex]

[tex]if \: \: m_{1} = m_{2} \: \: lines \: are \: parallel \\ [/tex]

[tex]if\:m_{1} = - \frac{1}{m_{2}} \\ lines \: are \: perpendicular \: to \: each \: other[/tex]

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MrRoyal MrRoyal · Answer 2 · 2021-10-26T15:12:21+02:00

Parallel lines have the same slope

The slope of a line is calculated as:

[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]

The slope of line 1 is:

[tex]\mathbf{m_1 = \frac{9 - 5}{-8 - 10}}[/tex]

[tex]\mathbf{m_1 = \frac{4}{-18}}[/tex]

[tex]\mathbf{m_1 = -\frac{2}{9}}[/tex]

Hence, the slope of line 1 is -2/9

The slope of line 2 is:

[tex]\mathbf{m_2 = \frac{-6 - -4}{11 - 2}}[/tex]

[tex]\mathbf{m_2 = \frac{-2}{9}}[/tex]

[tex]\mathbf{m_2 = -\frac{2}{9}}[/tex]

Hence, the slope of line 2 is -2/9

The lines have the same slope.

Hence, the two lines are parallel