Respuesta :
y = -1/2x + 12 is perpendicular to the line 2x - y = 4
What is a perpendicular line?
If four 90° angles are created at the junction of two lines, they are perpendicular.
We discover that[tex]y = (-1/2)*x + c[/tex] is a perpendicular line to the equation 2x - y = 4.
Any real value for c is allowed here.
A typical slope-intercept line looks like this:
[tex]y = a*x +b[/tex]
where b is the y-intercept and an is the slope.
This line's slope must be equal to the opposite of the inverse of the slope of any perpendicular line to it.
Consequently, the perpendicular line's slope should be:
a' = -(1/a).
Additionally, there are no limitations on the y-intercept of the perpendicular line, so you can choose any value for it.
Our initial line needs to be rewritten in the slope-intercept form at this point.
2x - y = 4
-2x + y = -4
y = 2x - 4
We now understand that this line's slope is a = 2.
The perpendicular one's slope will then be:
a' = -(1/a) = -1/2
The general shape of a line that is parallel to ours is then:
[tex]y = (-1/2)*x + c[/tex]
Where c can be any real value.
y = -1/2x + 12 is perpendicular to the line 2x - y = 4
To learn more about perpendicular lines refer to :
https://brainly.com/question/1202004
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