Answer:
[tex]y = -\frac{1}{2}x + 7[/tex]
Step-by-step explanation:
Given
[tex]2x - y = 5[/tex]
[tex]Point = (6,4)[/tex]
Required
Determine the equation of perpendicular line, r
First we need to determine the slope of the given equation
[tex]2x - y = 5[/tex]
Make y the subject:
[tex]y = 2x - 5[/tex]
The general form of an equation is:
[tex]y = mx + b[/tex]
Where:
[tex]m = slope[/tex]
By comparison;
[tex]m = 2[/tex]
Since both lines are perpendicular:
We have:
[tex]m_1 = -1/m[/tex] to calculate the slope of the perpendicular line
[tex]m_1 = -\frac{1}{2}[/tex]
Equation of the line can be solved using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex](x_1,y_1) = (6,4)[/tex]
[tex]m = m_1 = -\frac{1}{2}[/tex]
So: the equation becomes
[tex]y - 4 = -\frac{1}{2}(x - 6)[/tex]
[tex]y - 4 = -\frac{1}{2}x + 3[/tex]
Solve for y
[tex]y = -\frac{1}{2}x + 3 + 4[/tex]
[tex]y = -\frac{1}{2}x + 7[/tex]
Hence:
The required equation is
[tex]y = -\frac{1}{2}x + 7[/tex]
