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Solution - Finding a perpendicular line using slope-intercept form

y = - 0.143 x + 7.041

y=-0.143x+7.041

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Step-by-step explanation

1. Find the slope

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

$y = 7 x + 5$
$m = 7$

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 ( $m$ ):

$m_{p} \to - \frac{1}{m}$
$m = 7$

$m_{p} = - \frac{1}{7} = - 0.143$

3. Find the coordinates of the point where the lines intersect

Plug the y-coordinate of the intercept point into the line equation and solve for x:

$y = 7 x + 5$

$y = 7$

$7 = 7 \cdot x + 5$

$- 7 x = 5 - 7$

$- 7 x = - 2$

$x = - \frac{2}{-} 7$

$x = 0.286$

The coordinates of the point where the lines intersect are $(0.286, 7)$

4. Find the equation of the perpendicular line using slope-intercept form

To find the perpendicular line, plug its slope ( $- 0.143$ ) in for $m$ and the x and y-coordinates of the intercept point $(0.286, 7)$ in for $x$ and $y$ in the slope-intercept form, $y = m x + b$ , and solve for $b$ :

$m_{p} = - 0.143$
$y = 7$
$x = 0.286$

$y = m x + b$

$7 = - 0.143 \cdot 0.286 + b$

$7 = - 0.041 + b$

$b = 7 + 0.041$

$b = 7.041$

Plug $m_{p}$ and $b$ into the slope-intercept equation:

$y = m x + b$
$m_{p} = - 0.143$
$b = 7.041$
$y = - 0.143 x + 7.041$

The equation of the perpendicular line is $y = - 0.143 x + 7.041$

5. 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 slope-intercept form

Step-by-step explanation

1. Find the slope

2. Find the slope of a perpendicular line

3. Find the coordinates of the point where the lines intersect

4. Find the equation of the perpendicular line using slope-intercept form

5. Graph

Why learn this

Terms and topics

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Solution - Finding a perpendicular line using slope-intercept form

Step-by-step explanation

1. Find the slope

2. Find the slope of a perpendicular line

3. Find the coordinates of the point where the lines intersect

4. Find the equation of the perpendicular line using slope-intercept form

5. Graph

Why learn this

Terms and topics

Related links

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