The equation of the line that is perpendicular to the line y = 6 and passes through the point (-4,-3) is y = -3.
Given,
equation of line is y = 6
The required equation is perpendicular to the given line.
and it passes through the point (-4, -3)
=> p = -4 and q = -3
Comparing the given equation y = 6 with the slope intercept form of line equation, we get
y = mx + c
y = 0x + 6
=> c = 6 and m = 0
=> m1 = 0
We can find the slope of the perpendicular line by using the slope condition for perpendicular lines.
For two perpendicular lines,
m1 * m2 = -1
=> 0 * m2 = -1
=> m2 = 0
We can find the required equation of the perpendicular line using the following formula :
( y - yq ) = m ( x - xp )
For the perpendicular line, we have the equation.
Substituting the values in the above equation
=> ( y + 3 ) = 0 * ( x + 4 )
=> y + 3 = 0
=> y = -3
Therefore, using the slope intercept form of line equation and condition for slopes of perpendicular lines, we get the equation of the line that is perpendicular to the line y = 6 and passes through the point (-4,-3) as y = -3.
Learn more about Slope Intercept Form here:
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