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What is an equation in slope intercept form for the line perpendicular to y = - 2x + 5

that contains (-8, 1)?
1
A.O
y - 8 = 2 (x + 1)
B. O y=-2x - 1
C.O. 1
=
0:0 x = žy + 14

User Glasnt
by
7.6k points

1 Answer

1 vote

Answer:


\displaystyle y =(1)/(2)x+5

Explanation:

Equation of the line

The slope-intercept form of a line is given by:


y=mx+b

Being:

m = the slope of the line

b = the y-intercept

We can also use the point-slope form of the line:


y - k=m(x-h)

Being:

(h,k) = A point that belongs to the line

Two lines of slopes m1 and m2 are perpendicular if:


m_1.m_2=-1

We are given the line:


y=-2x+5

Whose slope is m1=-2

Thus, the perpendicular line has a slope of:


\displaystyle m_2=-(1)/(m_1)


\displaystyle m_2=-(1)/(-2)


\displaystyle m_2=(1)/(2)

The required line contains the point (-8,1), thus the equation is:


\displaystyle y - 1=(1)/(2)(x+8)

Removing the parentheses:


\displaystyle y - 1=(1)/(2)x+(1)/(2)\cdot 8

Adding 1:


\displaystyle y =(1)/(2)x+(1)/(2)\cdot 8+1

Operating:


\displaystyle y =(1)/(2)x+4+1


\mathbf{\displaystyle y =(1)/(2)x+5}

User Carl Younger
by
8.2k points