A design engineer is mapping out a new neighborhood with parallel streets. If one street passes through (4, 5) and (3, 2), what is the equation for a parallel street that passes through (2, −3)?

y = 3x + 11
y = 3x − 9
y equals negative 1 third times x plus 1
y equals negative 1 third times x minus 7 thirds

1 answer

To find the equation of the parallel street that passes through (2, -3), we first need to find the slope of the original street passing through (4, 5) and (3, 2).

Slope of the original street = (y2 - y1) / (x2 - x1)
= (2 - 5) / (3 - 4)
= -3 / -1
= 3

Since the parallel street has to have the same slope, the equation for the parallel street passing through (2, -3) is:

y = 3x + b

To find b, substitute the coordinates of (2, -3) into the equation:

-3 = 3(2) + b
-3 = 6 + b
b = -9

Therefore, the equation for the parallel street that passes through (2, -3) is:

y = 3x - 9

The correct answer is:
y = 3x - 9