Answer:
[tex]\displaystyle y =\frac{1}{2}x+5[/tex]
Step-by-step explanation:
Equation of the line
The slope-intercept form of a line is given by:
[tex]y=mx+b[/tex]
Being:
m = the slope of the line
b = the y-intercept
We can also use the point-slope form of the line:
[tex]y - k=m(x-h)[/tex]
Being:
(h,k) = A point that belongs to the line
Two lines of slopes m1 and m2 are perpendicular if:
[tex]m_1.m_2=-1[/tex]
We are given the line:
[tex]y=-2x+5[/tex]
Whose slope is m1=-2
Thus, the perpendicular line has a slope of:
[tex]\displaystyle m_2=-\frac{1}{m_1}[/tex]
[tex]\displaystyle m_2=-\frac{1}{-2}[/tex]
[tex]\displaystyle m_2=\frac{1}{2}[/tex]
The required line contains the point (-8,1), thus the equation is:
[tex]\displaystyle y - 1=\frac{1}{2}(x+8)[/tex]
Removing the parentheses:
[tex]\displaystyle y - 1=\frac{1}{2}x+\frac{1}{2}\cdot 8[/tex]
Adding 1:
[tex]\displaystyle y =\frac{1}{2}x+\frac{1}{2}\cdot 8+1[/tex]
Operating:
[tex]\displaystyle y =\frac{1}{2}x+4+1[/tex]
[tex]\mathbf{\displaystyle y =\frac{1}{2}x+5}[/tex]
