a Write an equation of a vertical line through the point 3 5

a) Write an equation of a vertical line through the point (-3, 5). b) Write an equation of a horizontal line through the point (-7, -2). c) Find the slope of a line parallel to the line with equation 3x - 7y = 21. d) Find the slope of a line perpendicular to the line with equation 2x + 3y = 5. e) Write an equation in point-slope for of the line through the point (-3, 2) perpendicular to the line with equation 2x + 3y = 5.

Solution

A.

Vertical line is given by:

x = C

Point (-3, 5)

equation of line will be:

x = -3

x + 3 = 0

B.

Horizontal line is given by:

y = C

Point = (-7, -2)

equation will be

y = -2

y + 2 = 0

C.

Standard equation:

y = mx + C

3x - 7y = 21

7y = 3x - 21

y = (3/7)x - 3

Slope = m = 3/7

D.

2x + 3y = 5

3y = -2x + 5

y = (-2/3)x + 5/3

Slope = m = (-2/3)

Slope of perpendicular line will be

m1*m = -1

m1*(-2/3) = -1

m1 = 3/2