Question

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

Answer 1

Answer:

$\displaystyle y =\frac{1}{2}x+5$

Step-by-step 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:

$\displaystyle m_2=-\frac{1}{m_1}$

$\displaystyle m_2=-\frac{1}{-2}$

$\displaystyle m_2=\frac{1}{2}$

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

$\displaystyle y - 1=\frac{1}{2}(x+8)$

Removing the parentheses:

$\displaystyle y - 1=\frac{1}{2}x+\frac{1}{2}\cdot 8$

Adding 1:

$\displaystyle y =\frac{1}{2}x+\frac{1}{2}\cdot 8+1$

Operating:

$\displaystyle y =\frac{1}{2}x+4+1$

$\mathbf{\displaystyle y =\frac{1}{2}x+5}$