Answer:
Step-by-step explanation:
The question is incomplete. find the complete question below;
A given line has the equation 2x + 12y = −1. What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9)? y = ( )x + 9
The equation of a line is represented as y = mx+c where m is the slope and c is the intercept. our ficus is to get both the slope and the intercept and then substitute then into the equation of the line.
First let us get the slope of the known line:
Rewriting the equation 2x + 12y = −1 in its standard form, we have;
12y = -2x-1
y = -1/6 x - 1/12
the slope of the line is -1/6
Since this line is perpendicular to the unknown line, the slope of the unknown line say M = -1/(-1/6) = 6
For the intercept
we will substitute the point (0,9) and the slope M = 6 into the equation
y = Mx+c to get the value of the intercept.
9 = 6(0)+c
c = 9
Finally, we will find the equation of the line perpendicular to the given line using the equation y = mx+c
Substituting m = 6 and c = 9 into the equation, we have y = 6x+9 or y-6x = 9
The unknown equation in slope intercept form is y=6x+9
The new equation of the perpendicular line is y = 6x + 9.
The slope of the line is determined from the given equation of the line.
[tex]2x + 12 y = -1\\\\12y = -1 - 2x\\\\y = \frac{-1}{12} - \frac{2x}{12} \\\\y = \frac{-1}{12} - \frac{x}{6}\\\\M = \frac{-1}{6}[/tex]
[tex]M_1 = \frac{-1}{M} = \frac{-1}{-1/6} = 6[/tex]
[tex]y = mx + c\\\\9 = 6(0) + c\\\\9 = c\\\\y = 6x + 9[/tex]
The complete question is below:
A given line has the equation 2x + 12y = −1. What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9)? y = ( )x + 9
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