Find the equation of the line passing through the point (6,3) that is perpendicular to the line 4x - 5y = -10?

Solution:

4x - 5y = -10

Transforming into the standard form of the straight line.

- 5y = 4x - 10

Divide both sides by -5

y = (4/-5)x - (10/-5)

y = (-4/5)x + 2

From the slope intercept form we get 

m = - 4/5

We know that

The slope of a perpendicular is a negative inverse of - 4/5

m = (5/4)

Slope intercept form for the perpendicular line is

y = (5/4) x +b

Solve for b using (6, 3)

3 = (5/4) (6) + b

3 = 30/4 + b

b = 3 - 30/4

b = (12 - 30)/4

b = -18/4

b = -9/2

So the perpendicular line is y = (5/4)x - 9/2

Therefore, the equation of the line is y = (5/4)x - 9/2.

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Find the equation of the line passing through the point (6,3) that is perpendicular to the line 4x − 5y = −10?

Summary:

The equation of the line passing through the point (6,3) that is perpendicular to the line 4x-5y=-10 is y = (5/4)x - 9/2.