Answer :
An equation in slope-intercept form for the line perpendicular to y = 3x + 9 that contains (-6, 3) is 3 = -1/3(-6) + 1.
What is slope-intercept form?
The most "popular" type of a straight line is one with a slope-intercept. Due to its simplicity, this is helpful to a lot of students. The slope and y-intercept of the straight line can be easily determined or read off from this form, making it possible to describe its properties without having access to the graph.
The equation for a line written in slope-intercept form
y = mx + b
Where,
m is the slope, and b is the y-intercept.
We know that the slope of a line perpendicular to given equation becomes reciprocal with opposite sign.
So, here slope is 3 and in perpendicular line it will become -1/3.
Now we will go with slope-intercept form and put the values (-6, 3) as x and y in y = mx + b
⇒ 3 = -1/3(-6) + b
Lets solve for b
⇒ b = 3 - ( -1/3(-6))
= 3 - (2)
= 1
Now we have the desired equation
3 = -1/3(-6) + 1
Thus, An equation in slope-intercept form for the line perpendicular to y = 3x + 9 that contains (-6, 3) is 3 = -1/3(-6) + 1.
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