perpendicular line equation

Question

Please show me the work-an equation of the line that is perpendicular to the given line -10x + 8y = 3 and passes through the given point (15, 12).

Answer 1

Slope - intercept form line equation is y = mx + b, where m is slope and b is y - intercept.

The line equation is - 10x + 8y = 3 and the point is (15, 12).

Write the equation in slope - intercept form.

8y = 10x + 3

y = (10/8)x + (3/8)

y = (5/4)x +(3/8).

Compare the equation with slope - intercept form y = mx + b.

slope = 5/4.

Because the slopes of perpendicular lines are negative reciprocals, the slope of perpendicular line through (15, 12) is - 4/5.

Now, the perpendecular line equation is y = (- 4/5)x + b.

Find the y - intercept by substituting the point in the line equation say (x, y) = (15, 12).

12 = (- 4/5)(15) + b

b = 12 + 12

⇒ b = 24.

The perpendecular line equation is y = (- 4/5)x + 24.