Write an equation of the line containing the point (o,-4) and perpendicular to the line y=1/3x+5
To find the equation of a line that is perpendicular to another line, we need to find the slope of the given line and then find the negative reciprocal.
The given line is y = (1/3)x + 5.
The slope of this line is 1/3 since it has the form y = mx + b, where m is the slope.
The negative reciprocal of 1/3 is -3/1, or simply -3.
Now, we have the slope of the line perpendicular to the given line, which is -3.
Next, substitute the given point (0, -4) and the calculated slope (-3) into the point-slope form of a linear equation, which is y - y₁ = m(x - x₁).
Using (0, -4) and -3, we get:
y - (-4) = -3(x - 0)
Simplifying the equation:
y + 4 = -3x
Rearranging the equation and bringing all terms to one side:
3x + y + 4 = 0
Therefore, the equation of the line containing the point (0, -4) and perpendicular to the line y = (1/3)x + 5 is 3x + y + 4 = 0.