Considering the definition of perpendicular line, the equation of the perpendicular line is y= 3/5x -2.
Linear equation
A linear equation o line can be expressed in the form y = mx + b.
where
- x and y are coordinates of a point.
- m is the slope.
- b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.
Perpendicular line
Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this case
In this case, the line is 5x+3y=15. Expressed in the form y = mx + b, you get:
3y= 15 - 5x
y= (-5x +15)÷ 3
y= -5/3x +5
If you multiply the slopes of two perpendicular lines, you get –1. So:
-5/3× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (-5/3)
slope perpendicular line= 3/5
The line passes through the point (5, 1). Replacing in the expression for a line:
1= 3/5× (5) + b
1= 3+ b
1 -3 = b
-2 = b
Finally, the equation of the perpendicular line is y= 3/5x -2.