Answer:
[tex]y =-\frac{1}{2}x + 8[/tex]
Step-by-step explanation:
Given
Perpendicular to [tex]y = 2x + 1[/tex]
Pass through [tex](4,6)[/tex]
Required
Determine the line equation
First, we need to determine the slope of [tex]y = 2x + 1[/tex]
An equation is of the form:
[tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
In this case:
[tex]m =2[/tex]
Next, we determine the slope of the second line.
Since both lines are perpendicular, the second line has a slope of:
[tex]m_1 = \frac{-1}{m}[/tex]
[tex]m_1 = \frac{-1}{2}[/tex]
[tex]m_1 = -\frac{1}{2}[/tex]
Since this line passes through (4,6); The equation is calculated as thus:
[tex]y - y_1 = m_1(x - x_1)[/tex]
Where
[tex](x_1,y_1) = (4,6)[/tex]
This gives:
[tex]y - 6=-\frac{1}{2}(x - 4)[/tex]
Open bracket
[tex]y - 6=-\frac{1}{2}x + 2[/tex]
Add 6 to both sides
[tex]y +6- 6=-\frac{1}{2}x + 2+6[/tex]
[tex]y =-\frac{1}{2}x + 8[/tex]
