Answer:
[tex]y = -5x+10[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (2,0)[/tex]
[tex]y = \frac{1}{5}x - 2[/tex]
Required
Determine an equation that perpendicular to the equation
An equation has the form:
[tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
By comparison:
[tex]m = \frac{1}{5}[/tex]
Next, we determine the slope of the new line.
When two lines are perpendicular, the following relation exist:
[tex]m_2= -\frac{1}{m_1}[/tex]
Substitute 1/5 for m1
[tex]m_2= -\frac{1}{1/5}[/tex]
[tex]m_2= -5[/tex]
The equation of the line is then calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where:
[tex]m_2= -5[/tex] and [tex](x_1,y_1) = (2,0)[/tex]
This gives:
[tex]y - 0 = -5(x - 2)[/tex]
[tex]y = -5(x - 2)[/tex]
[tex]y = -5x+10[/tex]
