Write equations of the lines that passes through the given point and is perpendicular to the graph of the given equations.

Question

• (-8,3); y+4=-2/3(x-2)

 

 

 

 

 

• (–9, 3); 3x + y = 5

 

 

 

 

 

 

 

 

 

• (0, –5); x – 6y = –2

 

 

 

Answer 1

1. Perpendicular lines have slopes that are negative reciprocals of each other.  Because the original line has a slope of m_original = -2/3, the new slope will be m_new = 3/2.

 

Use the new slope and the given point to find the y-intercept.

 

y = mx + b

3 = 3/2(-8) + b

3 = -12 + b

15 = b

 

Now, write the equation of the line using the new slope and y-intercept.

 

y = 3/2x + 15

 

2. Solve for y to rewrite the equation in slope-intercept form.

 

3x + y = 5

y = -3x + 5

 

m_original = -3        m_new = 1/3

 

Use the new slope and given point to find the y-intercept and write the equation in slope-intercept form.

 

y = mx + b

3 = 1/3(-9) + b

3 = -3 + b

6 = b

 

y = 1/3x + 6