Question

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

Answer 1

`\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}`