Answer:
[tex]\displaystyle y=\frac{1}{2}x-7[/tex]
Step-by-step explanation:
Perpendicular Lines
Two lines of slopes m1 and m2 are perpendicular if their slopes meet the condition:
[tex]m_1\cdot m_2=-1\qquad \qquad [1][/tex]
The slope-intercept form of a line with slope m and y-intercept of b is:
[tex]y=mx+b[/tex]
The point-slope form of a line with slope m that passes through the point (h,k) is:
[tex]y-k=m(x-h)[/tex]
We are given the line
[tex]y=-2x+4[/tex]
From which we can know the value of the slope is m1=-2
The slope of the required line m2 can be calculated from [1]
[tex]\displaystyle m_2=-\frac{1}{m_1}=-\frac{1}{-2}=\frac{1}{2}[/tex]
Now we know the slope and the point (8,-3) through which our line goes, thus:
[tex]\displaystyle y-(-3)=\frac{1}{2}(x-8)[/tex]
To find the slope-intercept form, operate:
[tex]\displaystyle y+3=\frac{1}{2}x-\frac{1}{2}\cdot 8[/tex]
[tex]\displaystyle y=\frac{1}{2}x-4-3[/tex]
[tex]\mathbf{\displaystyle y=\frac{1}{2}x-7}[/tex]
