Answer:
[tex]y=2x-3[/tex]
Skills needed: Point-Slope, Linear Equations
Step-by-step explanation:
1) We are given [tex]y=-\frac{1}{2}x-1[/tex], and we need to find a perpendicular line to this that also passes through the point [tex](6,9)[/tex].
- First, we can use the fact that the perpendicular slope is the negative reciprocal of the original slope.
---> This means that [tex]m*m_p=-1[/tex] (original slope x perpendicular slope = -1) This means that [tex]-\frac{1}{2}*m_p=-1[/tex]
In order to isolate [tex]m_p[/tex], we multiply both sides by [tex]-2[/tex]
[tex]m_p=-1*-2[/tex] --> [tex]m_p=2[/tex].
The slope of the perpendicular line is 2.
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2) Next, we can use point-slope form.
[tex]y-y_1=m(x-x_1)[/tex]
Given [tex]m[/tex] and a coordinate point of [tex](x_1,y_1)[/tex].
[tex]m[/tex] is the slope
[tex]x_1[/tex] is x value of coordinate point
[tex]y_1[/tex] is y value of coordinate point
Let's evaluate below:
---> [tex]y-9=2(x-6)[/tex]
distribute on right side: [tex]y-9=2x-12[/tex]
add 6 to both sides: [tex]y=2x-3[/tex]
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[tex]y=2x-3[/tex] is your answer! Have a nice day!
