Question

Tell whether the lines through the given points are parallel, perpendicular, or neither?

Answer 1

$Slope\,\,1=\frac{-1}{slope\,\,2}$

So, Both lines are perpendicular

Step-by-step explanation:

We need to identify if lines:

Line 1: (8,12)(7,-5)

Line 2: (-9,3)(8,2)

are parallel, perpendicular, or neither?

• Lines are parallel if they have same slopes i.e slope 1= slope2
• Lines are perpendicular if their slopes are negative inverses of each other i.e slope 1= -1/slope 2

The formula used to find slope is:

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

Finding Slope of Line 1:

The points are: Line 1: (8,12)(7,-5)

$x_1=8, y_1=12, x_2=7,y_2=-5$

Putting values in the formula:

$Slope\,\,1=\frac{y_2-y_1}{x_2-x_1}$

$Slope\,\,1=\frac{-5-(12)}{7-8}$

$Slope\,\,1=\frac{-5-12}{-1}$

$Slope\,\,1=\frac{-17}{-1}$

$Slope\,\,1=17$

So, Slope of line 1 is 17

Finding Slope of Line 2:

The points are: Line 2: (-9,3)(8,2)

$x_1=-9, y_1=3, x_2=8,y_2=2$

Putting values in the formula:

$Slope\,\,2=\frac{y_2-y_1}{x_2-x_1}$

$Slope\,\,2=\frac{2-(3)}{8-(-9)}$

$Slope\,\,2=\frac{2-3}{8+9}$

$Slope\,\,2=\frac{-1}{17}$

So, Slope of line 2 is $\frac{-1}{17}$

Since $Slope\,\,1=\frac{-1}{slope\,\,2}$

So, Both lines are perpendicular

Keywords: Slope of Lines

Learn more about Slope of lines at:

• brainly.com/question/9369548
• brainly.com/question/4932386
• brainly.com/question/4097107

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