Solution - Finding a perpendicular line using point-slope form

y = - 0.333 x + 1.333

y=-0.333x+1.333

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Step-by-step explanation

1. Find the slope

To find the slope $(m)$ , use the equation for slope-intercept form:
$y = m x + b$

$y = 3 x - 2$
$m = 3$

2. Find the slope of a perpendicular line

The slope of a perpendicular line ( $m_{p}$ ) is the negative reciprocal (inverse) of the original slope ( $m$ ):

$m_{p} \to - \frac{1}{m}$
$m = 3$

$m_{p} = - \frac{1}{3} = - 0.333$

3. Find the equation of the perpendicular line using the point slope form

To find the perpendicular line, plug its slope ( $- 0.333$ ) in for $m$ and the x and y-coordinates of the given point on the line $(1, 1)$ in for $x_{1}$ and $y_{1}$ in the point-slope form:
$(y - y_{1}) = m (x - x_{1})$

$m_{p} = - 0.333$
$y_{1} = 1$
$x_{1} = 1$

$(y - y_{1}) = m (x - x_{1})$

$y - 1 = - 0.333 (x - 1)$

$y - 1 = - 0.333 x + 0.333$

$y = - 0.333 x + 0.333 + 1$

$y = - 0.333 x + 1.333$

The equation of the perpendicular line is $y = - 0.333 x + 1.333$

4. Graph

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Why learn this

Whether they are horizontal, vertical, diagonal, parallel, perpendicular, intersecting, or tangent lines, it is a fact of life that straight lines are everywhere. Chances are, you know what a line is, but it is also important to understand their formal definition in order to better understand the various problems that involve them. A line is a one-dimensional figure, with a length but no width, that connects two points. After points, lines are the second smallest building blocks of shapes, which are essential for understanding our world and the spaces we find ourselves in. Additionally, understanding the slope, direction, and behavior of different types of lines is necessary for graphing and understanding certain types of information, an important skill across many industries.

Solution - Finding a perpendicular line using point-slope form

Step-by-step explanation

1. Find the slope

2. Find the slope of a perpendicular line

3. Find the equation of the perpendicular line using the point slope form

4. Graph

Why learn this

Terms and topics

Related links

Solution - Finding a perpendicular line using point-slope form

Step-by-step explanation

1. Find the slope

2. Find the slope of a perpendicular line

3. Find the equation of the perpendicular line using the point slope form

4. Graph

Why learn this

Terms and topics

Related links

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