Respuesta :
Answer:
y = 6x + 9
Step-by-step explanation:
The equation of a line in slope- interceot form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 2x + 12y = - 1 into this form
Subtract 2x from both sides
12y = - 2x - 1 ( divide all terms by 12 )
y = - [tex]\frac{1}{6}[/tex] x - [tex]\frac{1}{12}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{1}{6}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{6} }[/tex] = 6
Note the line passes through (0, 9) on the y- axis ⇒ c = 9
y = 6x + 9 ← equation of perpendicular line
Answer:
[tex]y=6x+9[/tex]
Step-by-step explanation:
Given equation of the line,
[tex]2x + 12y = -1[/tex]
[tex]12y=-2x-1[/tex]
[tex]y=-\frac{1}{6}x-\frac{1}{12}[/tex]
Slope intercept form of a line is y = mx + c,
Where, m is the slope of the line,
By comparing, the slope of the given line is [tex]\frac{-1}{6}[/tex],
Since, when two lines are perpendicular then the product of their slope is -1,
Let [tex]m_1[/tex] be the slope of the perpendicular line of the given line,
[tex]m_1\times -\frac{1}{6}=-1[/tex]
[tex]\implies m_1=6[/tex]
Now, point slope intercept form of a line is,
[tex]y_y_1=m(x-x_1)[/tex]
Where, [tex](x_1, y_1)[/tex] is the point on the line,
Hence, the equation of the line passes through the point (0, 9) and having slope 6 is,
[tex]y-9=6(x-0)[/tex]
[tex]y-9=6x[/tex]
[tex]y=6x+9[/tex]
