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Solution - Properties of a line from point and slope

Line equation in slope-intercept form

y = - 6 x - 6

y=-6x-6

Slope

m = - 6

m=-6

x-intercept

(- 1, 0)

(-1,0)

y-intercept

(0, - 6)

(0,-6)

See steps

Step-by-step explanation

1. Find the equation of the line in slope-intercept form

Plug the slope ( $m$ ) into the equation for slope-intercept form:
$y = m x + b$

$y = m x + b$

$m = - 6$

$y = - 6 x + b$

Plug the x and y-coordinates of the given point into the equation and solve for $b$ , since we already have -intercept, x-coordinate is zero:

$0 = - 6 \cdot - 1 + b$

$0 = 6 + b$

$b = 0 - 6$

$b = - 6$

Plug $m$ and $b$ into the equation for slope-intercept form:
$y = m x + b$

$y = m x + b$

$m = - 6$
$b = - 6$

$y = - 6 x - 6$

The equation of the line in slope-intercept form is: $y = - 6 x - 6$

2. Find the x and y-intercepts

To find the x-intercept, plug $0$ in for $y$ in the equation, $y = - 6 x - 6$ , and solve for $x$ :

$y = - 6 x - 6$

$0 = - 6 x - 6$

$6 x = - 6$

$x = - \frac{6}{6}$

$x = - 1$

x-intercept $= (- 1, 0)$

To find the y-intercept, plug $0$ in for $x$ in the equation, $y = - 6 x - 6$ , and solve for $y$ :

$y = - 6 x - 6$

$y = - 6 \cdot 0 - 6$

$y = - 6$

y-intercept $= (0, - 6)$

The $b$ in the slope-intercept form equation, $y = m x + b$ , is always equal to the y-coordinate of the y-intercept point. In other words, if $x = 0$ then $y = b$

3. Graph of the line equation

$y = - 6 x - 6$

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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.

Terms and topics

Properties of a straight lines

Solution - Properties of a line from point and slope

Step-by-step explanation

1. Find the equation of the line in slope-intercept form

2. Find the x and y-intercepts

3. Graph of the line equation

Why learn this

Terms and topics

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