Answer:
The answer is
[tex]y = \frac{5}{2} x - 4[/tex]
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the perpendicular line we must first find the slope of the original line
The original line is y = - 2/5x + 3
Comparing with the general equation above
Slope/m = - 2/5
Since the lines are perpendicular to each other the slope of the perpendicular line is the negative inverse of the original line
So we have
[tex]m \times m _1 = - 1 \\ - \frac{2}{5} m _1 = - 1 \\ = - 2m _1 = - 5 \\ = m _1 = \frac{5}{2} [/tex]
So the slope of the perpendicular line is
5/2
So the equation of the line using point
(2, 1) and slope 5/2 is
[tex]y - 1 = \frac{5}{2} (x - 2) \\ y - 1 = \frac{5}{2} x - 5 \\ y = \frac{5}{2} x - 5 + 1[/tex]
We have the final answer as
[tex]y = \frac{5}{2} x - 4[/tex]
Hope this helps you
