Question

The streets in Mid Town are laid out on a grid, If Oak St can be represented by the equation 6x+ 18y= 5.

Which of the following equations represents a line perpendicular to Oak St (6x + 18y = 5)?
a) y = 3x - 10
b) y + 6 = 3(x - 15)
c) x = 3
d) 2x - 3y = 5

Answer 1

To find the equation of a line perpendicular to Oak St, you need to find the negative reciprocal of the slope of Oak St and look for an equation with that slope. Option (b) y + 6 = 3(x - 15) in the given choices fits this criterion.

Step-by-step explanation:

To find an equation of a line perpendicular to the given line, we need to find the negative reciprocal of the slope of the given line. The slope of the given line is 3/18, so the negative reciprocal is -18/3 = -6.

Therefore, the equation of the line perpendicular to Oak St is y = -6x + b, where b is a constant.

Out of the given options, option (a) y = 3x - 10 and option (d) 2x - 3y = 5 do not have a slope of -6, so they are not perpendicular to Oak St.

Option (c) x = 3 is not an equation of a line in slope-intercept form, so it is also not perpendicular to Oak St.

Therefore, option (b) y + 6 = 3(x - 15) represents a line perpendicular to Oak St.