Write the equation of the line satisfying the given condition.
Perpendicular to y = 4x + 2 and passing through the point (0, -4)
(Hint: Slopes of non-vertical perpendicular lines are negative reciprocal of each other.)
The equation of the new line can be stated as
y = (-1/4)x -4
without doing any calculations.
y = 4x + 2. (0,-4).
m = 4.
m2 = -1/4.
y = (-1/4)*0 + b = -4,
b = -4.
Eq: y = (-1/4)x - 4.
Why doesn it nee
Why does it need to be -4?
To find the equation of a line perpendicular to a given line, we need to consider two things: the slope of the given line and the negative reciprocal of that slope.
Given:
The given line has the equation y = 4x + 2.
Step 1: Determine the slope of the given line.
The given line is in the form y = mx + b, where m represents the slope of the line. In this case, the slope is 4.
Step 2: Find the negative reciprocal of the slope.
To find the negative reciprocal, we take the reciprocal (1/m) of the slope and then multiply it by -1. In this case, the negative reciprocal of 4 is -1/4.
Step 3: Use the negative reciprocal slope and the given point to write the equation of the perpendicular line.
We have the slope (-1/4) and the point (0, -4). We can use the point-slope form of a linear equation to write the equation of the line.
The point-slope form is given by: y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Substituting the values, we get:
y - (-4) = (-1/4)(x - 0)
Simplifying:
y + 4 = (-1/4)x
Rearranging the equation to the standard form, we get:
1/4x + y + 4 = 0
Thus, the equation of the line perpendicular to y = 4x + 2 and passing through the point (0, -4) is 1/4x + y + 4 = 0.