The equation of the perpendicular line is: y = 5/3x - 6.
To find the perpendicular equation to y = -3/5x - 6, we need to take the reciprocal of the slope and multiply it by negative 1.
Here's how we get there:
Slope: The slope of the given equation is -3/5.
Reciprocal: The reciprocal of -3/5 is -5/3.
Negative reciprocal: Multiplying the reciprocal by -1 gives us 5/3.
Perpendicular equation: Therefore, the equation of the perpendicular line will be:
y = 5/3x + b
where b is the y-intercept.
We still need to find the y-intercept (b) to completely define the equation.
Here are two ways to find the y-intercept:
Method 1: Point-slope form
Choose a point on the original line. Let's use the y-intercept (0, -6).
Substitute this point into the equation of the perpendicular line:
-6 = 5/3 * 0 + b
-6 = 0 + b
-6 = b
Therefore, the y-intercept is -6.
Method 2: Slope-intercept form
Rewrite the original equation in slope-intercept form: y = -3/5x - 6
Since the perpendicular line intersects the original line, they share the same y-intercept (b) which is -6.
Therefore, the equation of the perpendicular line is: y = 5/3x - 6 .
Question
what would be the perpendicular equation to y=-3/5x-6 ?