Step-by-step explanation:
4x -y =2
-y = -4x + 2
y = 4x -2
slope = 4
perpendicular slope is negative inverse
so -1/4
y- -2 = -1/4(x - 4)
y+2 = -1/4x +1
y = -1/4x -1
As per slope-intercept form, the equation of a line perpendicular to
4x - y = 2 that contains the point (4,−2) is x + 4y + 4 = 0.
The slope-intercept form of a straight line is y = mx + c.
Here, 'm' is the slope and 'c' ix the y-intercept of the given line.
The given equation is 4x - y = 2
Therefore, in slope-intercept form, this equation will be:
y = 4x - 2
Therefore, the slope of this line is m = 4.
The required line is perpendicular to the given line.
Therefore, the slope of the required line is
= - 1/m
= - 1/4
Again, the required line passes through the point (4, - 2).
Therefore, - 2 = - (1/4)4 + c
⇒ c = - 2 + 1
⇒ c = - 1
The equation of the required line is
y = - (1/4)x - 1
⇒ 4y = - x - 4
⇒ x + 4y + 4 = 0
Learn more about the slope-intercept form of a straight line here: brainly.com/question/14534555
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