Write an equation in slope-intercept form for the line that passes through (-3, 5), and is perpendicular to the graph of 5x - 6y = 9

Answer 1

Perpendicular lines have negative, reciprocal slopes.

Step1: Find the slope of the line that you were given

5x - 6y = 9

5x = 6y + 9

5x - 9 = 6y

(5/6)x - 3/2 = y or y = (5/6)x - 3/2

Slope = 5/6

Step 2: Flip and Change sign of slope to find the slope of perpendicular line

New Slope = -6/5

Step 3: Use New Slope and Given Point to write the equation of the perpendicular line

New Slope = -6/5 Given Point: (-3,5)

y = mx + b

y = (-6/5)x + b

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

5 = 18/5 + b (Multiply through by 5 to clear fractions)

25 = 18 + 5b

7 = 5b

7/5 = b

Step 4: Write the equation (Answers)

y = (-6/5)x +7/5

Answer 2

When 2 lines are perpendicular, they have slopes that are negative reciprocals of each other.

For example, suppose you were trying to find the equation of the line that passes through (1,1) and is perpendicular to 3x + 2y = -7.

The first step is to find the slope of the given line by solving the equation for y to get y = -(3/2)x - (7/2). This line has slope (-3/2), so the perpendicular line will have slope 2/3, so it will have the form y = (2/3)x + b. Substitute the given point into this equation to find b:

1 = (2/3)(1) + b ==> b = 1/3, so the equation of the perpendicular line is y = (2/3)x + (1/3)